chapters 1 6 and chapter 7 sections 1 4 short …...the graph shows the depreciation of the...

PrecalculusFall Final ReviewChapters 1-6 and Chapter 7 sections 1-4 Name___________________________________

SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!

Graph the equation using a graphing utility. Use agraphing utility to approximate the intercepts roundedto two decimal places, if necessary. Use the TABLEfeature to help establish the viewing window.

1) 3x - 4y = 56

Find the midpoint of the line segment joining the pointsP1 and P2.

2) P1 = (-0.6 , -0.2); P2 = (-2.4, -1.8 )

Find the center (h, k) and radius r of the circle with thegiven equation.

3) x2 + 18x + 81 + y2 + 4y + 4 = 36

Decide whether or not the points are the vertices of aright triangle.

4) (9, -6), (15, -4), (14, -9)

Solve the equation algebraically. Verify your solutionwith a graphing utility.

5) x2 - 11x + 30 = 0

Graph the equation.6) x2 + (y - 2)2 = 16

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Solve.7) A vendor has learned that, by pricinghot dogs at $1.25 , sales will reach 79 hot dogsper day. Raising the price to $2.00 will causethe sales to fall to 46 hot dogs per day. Let ybe the number of hot dogs the vendor sells atx dollars each. Write a linear equation thatrelates the number of hot dogs sold per day,y, to the price x.

List the intercepts for the graph of the equation.8) y2 = x + 9

Find the slope of the line containing the two points.9) (-9, 6); (-9, 5)

Graph the equation by plotting points.10) x = y2

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Find the distance d(P1, P2) between the points P1 and P2.11) P1 = (7, -7); P2 = (3 , -5)

Graph the equation using a graphing utility. Use agraphing utility to approximate the intercepts roundedto two decimal places, if necessary.

12) 3x2 - 5y = 34

1

Find the center (h, k) and radius r of the circle. Graph thecircle.

13) x2 + y2 + 6x + 12y + 36 = 0

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Write the standard form of the equation of the circle withradius r and center (h, k).

14) r = 2; (h, k) = (0, -2)

Solve.15) A school has just purchased new computer

equipment for $17,000 .00. The graph showsthe depreciation of the equipment over 5years. The point (0, 17,000 ) represents thepurchase price and the point (5, 0) representswhen the equipment will be replaced. Write alinear equation in slope-intercept form thatrelates the value of the equipment, y, to yearsafter purchase x . Use the equation to predictthe value of the equipment after 2 years.

x2.5

y225002000017500150001250010000750050002500

x2.5

y225002000017500150001250010000750050002500

Find the slope and y-intercept of the line.16) 4x - 7y = 1

Find the slope of the line and sketch its graph.17) 3x + 5y = 26

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Solve.18) When making a telephone call using a calling

card, a call lasting 6 minutes cost $1.95 . Acall lasting 14 minutes cost $3.95 . Let y be thecost of making a call lasting x minutes using acalling card. Write a linear equation thatrelates the cost of a making a call, y, to thetime x.

Plot the point in the xy-plane. Tell in which quadrant oron what axis the point lies.

19) (0, -1)

x-5 5

y

5

-5

x-5 5

y

5

-5

Use a graphing utility to approximate the real solutions,if any, of the equation rounded to two decimal places.

20) x4 - 3x2 + 4x + 15 = 0

Write the equation of a function that has the givencharacteristics.

21) The graph of y = x2, shifted 7 units downward

2

Use a graphing utility to graph the function over theindicated interval and approximate any local maximaand local minima. If necessary, round answers to twodecimal places.

22) f(x) = x3 - 3x2 + 1; (-5, 5)

Graph the function by starting with the graph of thebasic function and then using the techniques of shifting,compressing, stretching, and/or reflecting.

23) f(x) = 14x3

x-5 5

y

5

-5

x-5 5

y

5

-5

The graph of a function f is given. Use the graph toanswer the question.

24) Is f(3) positive or negative?

5

-5 5

-5

Find the average rate of change for the function betweenthe given values.

25) f(x) = x2 + 2x; from 4 to 8

Determine algebraically whether the function is even,odd, or neither.

26) f(x) = 1x2

Answer the question about the given function.

27) Given the function f(x) = x2 + 2x - 4

, list the

x-intercepts, if any, of the graph of f.

The graph of a function is given. Decide whether it iseven, odd, or neither.

28)

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

Solve the problem.29) It has been determined that the number of

fish f(t) that can be caught in t minutes in acertain pond using a certain bait isf(t) = 0.27t + 1, for t > 10. Find theapproximate number of fish that can becaught if you fish for 20 minutes.

Locate any intercepts of the function.30) f(x) = -3x + 4 if x < 1

4x - 3 if x ≥ 1

For the graph of the function y = f(x), find the absolutemaximum and the absolute minimum, if it exists.

31)

3

MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.

Match the function with the graph that best describesthe situation.

32) The amount of rainfall as a function of time, ifthe rain fell more and more softly.A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y



33)

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

Find the value for the function.

34) Find f(2) when f(x) = x2 - 6x + 1

.

4


Match the correct function to the graph.35)

x-5 5

y

5

-5

x-5 5

y

5

-5

A) y = |2 - x| B) y = |x + 2|C) y = |1 - x| D) y = x - 2



36)

x-π

-π2

π2 π

y54321

-1-2-3-4-5

x-π

-π2

π2 π

y54321

-1-2-3-4-5

For the given functions f and g, find the requestedfunction and state its domain.

37) f(x) = 5 - x; g(x) = x - 1Find f ∙ g.


38)

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

x-10 -8 -6 -4 -2 2 4 6 8 10

y108642

-2-4-6-8

-10

The graph of a function f is given. Use the graph toanswer the question.

39) For what numbers x is f(x) = 0?

100

-100 100

-100


Match the graph to the function listed whose graph mostresembles the one given.

40)

A) reciprocal functionB) square root functionC) absolute value functionD) square function

5


Solve the problem.41) To convert a temperature from degrees

Celsius to degrees Fahrenheit, you multiplythe temperature in degrees Celsius by 1.8 andthen add 32 to the result. Express F as a linearfunction of c.

Graph the function using its vertex, axis of symmetry,and intercepts.

42) f(x) = 4x2 - 32x + 65

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Find the vertex and axis of symmetry of the graph of thefunction.

43) f(x) = -x2 + 4x

Solve the problem.44) A rock falls from a tower that is 160 ft high.

As it is falling, its height is given by theformula h = 160 - 16t2. How many secondswill it take for the rock to hit the ground (h =

0)?

45) The quadratic functionf(x) = 0.0037x2 - 0.43 x + 36.17 models themedian, or average, age, y, at which U.S. menwere first married x years after 1900. In whichyear was this average age at a minimum?(Round to the nearest year.) What was theaverage age at first marriage for that year?(Round to the nearest tenth.)

46) A developer wants to enclose a rectangulargrassy lot that borders a city street forparking. If the developer has 304 feet offencing and does not fence the side along thestreet, what is the largest area that can beenclosed?


47) f(x) = x2 + 12x

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

Determine the quadratic function whose graph is given.48)

x

y

(-2, -1)

(0, 3)

x

y

(-2, -1)

(0, 3)

6

Solve the problem.49) The following scatter diagram shows heights

(in inches) of children and their ages.

Height (inches)

x1 2 3 4 5 6 7 8 9 10 11 12 13 14

y66

60

54

48

42

36

30

24

18

12

6

x1 2 3 4 5 6 7 8 9 10 11 12 13 14

y66

60

54

48

42

36

30

24

18

12

6

Age (years)

What happens to height as age increases?

Graph the function. State whether it is increasing,decreasing, or constant..

50) f(x) = 5x + 3

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

Solve the problem.51) The cost in millions of dollars for a company

to manufacture x thousand automobiles isgiven by the function C(x) = 4x2 - 24x + 81.Find the number of automobiles that must beproduced to minimize the cost.

Graph the function f by starting with the graph of y = x2and using transformations (shifting, compressing,stretching, and/or reflection).

52) f(x) = -x2 + 6x - 3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Solve the inequality.53) 9x2 + 64 < 48x


54) f(x) = -x2 + 2x + 8

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

7

Plot a scatter diagram.55) Draw a scatter diagram of the given data.

Find the equation of the line containing thepoints (2.2, 8.1) and (4.6 , 3.0 ). Graph the lineon the scatter diagram.

x 1.4 2.2 2.8 3.6 4.6y 9.5 8.1 5.7 4.6 3.0

x1 2 3 4 5

y14

12

10

8

6

4

2

x1 2 3 4 5

y14

12

10

8

6

4

2

Use a graphing utility to find the equation of the line ofbest fit. Round to two decimal places, if necessary.

56) Managers rate employees according to jobperformance and attitude. The results forseveral randomly selected employees aregiven below.

PerformanceAttitude

59 63 65 69 58 77 76 69 70 6472 67 78 82 75 87 92 83 87 78

Solve the problem.57) A flare fired from the bottom of a gorge is

visible only when the flare is above the rim. Ifit is fired with an initial velocity of 176 ft/sec,and the gorge is 480 ft deep, during whatinterval can the flare be seen?(h = -16t2 + v0t + h0.)

Determine the average rate of change for the function.58) F(x) = -5

Graph the function f by starting with the graph of y = x2and using transformations (shifting, compressing,stretching, and/or reflection).

59) f(x) = x2 + 8x + 7

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Determine the average rate of change for the function.60) p(x) = -x + 8

Use the graph to find the vertical asymptotes, if any, ofthe function.

61)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

List the potential rational zeros of the polynomialfunction. Do not find the zeros.

62) f(x) = 6x4 + 4x3 - 2x2 + 2

Use the Rational Zeros Theorem to find all the real zerosof the polynomial function. Use the zeros to factor f overthe real numbers.

63) f(x) = x4 - 12x2 - 64

8

Graph the function using transformations.

64) f(x) = 1x

- 3

x-5 5

y

5

-5

x-5 5

y

5

-5

State whether the function is a polynomial function ornot. If it is, give its degree. If it is not, tell why not.

65) f(x) = x( x -14)

Solve the problem.66) For what positive numbers will the cube of a

number exceed 9 times its square?

Find the indicated intercept(s) of the graph of thefunction.

67) y-intercept of f(x) = (x - 6)2

(x + 11)3


68) f(x) = 3x4 - 6x3 + 4x2 - 2x + 1


69) y-intercept of f(x) = x - 7x2 + 11x - 12

Give the equation of the horizontal asymptote, if any, ofthe function.

70) g(x) = x2 + 8x - 5x - 5

Solve the inequality algebraically. Express the solutionin interval notation.

71) x2(x - 11)(x + 1)(x - 4)(x + 8)

≥ 0

For the polynomial, list each real zero and itsmultiplicity. Determine whether the graph crosses ortouches the x-axis at each x -intercept.

72) f(x) = 13x2(x2 - 5 )


73) f(x) = 3x3 - 2x2 + 6x - 4

Find the x- and y-intercepts of f.74) f(x) = (x + 6)(x - 4)(x + 4)

Give the equation of the oblique asymptote, if any, ofthe function.

75) h(x) = 3x2 - 7x - 2

6x2 - 9x + 9

Use the graph to find the vertical asymptotes, if any, ofthe function.

76)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Find the intercepts of the function f(x).77) f(x) = 4x - x3


78) y-intercept of f(x) = 5xx2 - 19

9

State whether the function is a polynomial function ornot. If it is, give its degree. If it is not, tell why not.

79) f(x) = 1 + 9x

Use the graph of the function f to solve the inequality.80) f(x) < 0

x-10 -8 -6 -4 -2 2 4 6 8 10

y

x-10 -8 -6 -4 -2 2 4 6 8 10

y

Find the domain of the composite function f ∘ g.

81) f(x) = 2x + 1

; g(x) = x + 10

Solve the problem.82) During its first year of operation, 200,000

people visited Rave Amusement Park. Sixyears later, the number had grown to 834,000.If the number of visitors to the park obeys thelaw of uninhibited growth, find theexponential growth function that models thisdata.

83) Between 7:00 AM and 8:00 AM, trains arriveat a subway station at a rate of 10 trains perhour (0.17 trains per minute). The followingformula from statistics can be used todetermine the probability that a train willarrive within t minutes of 7:00 AM.

F(t) = 1 - e-0.17tDetermine how many minutes are needed forthe probability to reach 40%.

Solve the equation.84) log3 (x + 2) = 2 + log3 (x - 3 )

85) 17x

= 49

Solve the problem.86) f(x) = log3(x + 1) and g(x) = log3(x - 4).

Solve g(x) = 129. What point is on the graphof g?

Solve the equation.

87) 32x

= 827

88) log3 x + log3(x - 24) = 4

Write as the sum and/or difference of logarithms. Expresspowers as factors.

89) log 1 - 1x3

Solve the problem.90) The long jump record, in feet, at a particular

school can be modeled byf(x) = 18.2 + 2.4 ln(x + 1) where x is the numberof years since records began to be kept at theschool. What is the record for the long jump15 years after record started being kept?Round your answer to the nearest tenth.

For the given functions f and g, find the requestedcomposite function value.

91) f(x) = 7x + 8, g(x) = -1/x; Find (g ∘ f)(3).

Use transformations to graph the function. Determinethe domain, range, and horizontal asymptote of thefunction.

92) f(x) = 5-x + 2

x-4 -2 2 4 6

y

4

2

-2

-4

x-4 -2 2 4 6

y

4

2

-2

-4

10

Solve the problem.93) The formula P = 14.7e-0.21x gives the

average atmospheric pressure, P, in poundsper square inch, at an altitude x, in milesabove sea level. Find the average atmosphericpressure for an altitude of 2.3 miles. Roundyour answer to the nearest tenth.

Express as a single logarithm.94) 7ln (x - 8) - 2 ln x


The graph of a logarithmic function is shown. Select thefunction which matches the graph.

95)

x-5 5

y

5

-5

x-5 5

y

5

-5

A) y = log x - 2 B) y = 2 - log xC) y = log(2 - x) D) y = log(x - 2)


Express as a single logarithm.96) log x + log (x2 - 169) - log 9 - log (x - 13)

Solve the equation.97) log11 x2 = 4

Solve the problem.98) Gillian has $10,000 to invest in a mutual fund.

The average annual rate of return for the pastfive years was 12.25%. Assuming this rate,determine how long it will take for herinvestment to double.

Decide whether the composite functions, f ∘ g and g ∘ f,are equal to x.

99) f(x) = x , g(x) = x2

Solve the problem.100) A fully cooked turkey is taken out of an oven

set at 200 °C (Celsius) and placed in a sink ofchilled water of temperature 4°C. After 3minutes, the temperature of the turkey ismeasured to be 50°C. How long (to thenearest minute) will it take for thetemperature of the turkey to reach 15°C?Assume the cooling follows Newton's Law ofCooling:

U = T + (Uo - T)ekt.(Round your answer to the nearest minute.)

Find the period.101) y = -5 cos(5πx + 4)

Solve the problem.102) Before exercising, an athlete measures her air

flow and obtains

a = 0.65 sin 2π5t

where a is measured in liters per second and tis the time in seconds. If a > 0, the athlete isinhaling; if a < 0, the athlete is exhaling. Thetime to complete one completeinhalation/exhalation sequence is arespiratory cycle. What is the amplitude? What is the period?What is the respiratory cycle? Graph a over two periods beginning at t = 0.

t5 10

a1

-1

t5 10

a1

-1

11

Convert the angle in degrees to radians. Express theanswer as multiple of π.

103) 87°

Find an equation for the graph.104)

Solve the problem.105) For what numbers θ is f(θ) = csc θ not

defined?

Find the phase shift.

106) y = -3 sin 14x - π

4

If A denotes the area of the sector of a circle of radius rformed by the central angle θ, find the missing quantity.If necessary, round the answer to two decimal places.

107) r = 88.4 centimeters, θ = π5

radians, A = ?

Use the even-odd properties to find the exact value ofthe expression. Do not use a calculator.

108) sec - π6

Convert the angle in radians to degrees.

109) - 7π6

Solve the problem.110) A rotating beacon is located 4 ft from a wall.

If the distance from the beacon to the point onthe wall where the beacon is aimed is givenby a = 4|sec (2πt)| , where t is in seconds,find a when t = 0.40 seconds. Round youranswer to the nearest hundredth.

Find the exact value. Do not use a calculator.111) cot 45 °

Use the properties of the trigonometric functions to findthe exact value of the expression. Do not use a calculator.

112) sin2 55° + cos2 55°

Find the amplitude.

113) y = -3 cos 4x + π2

In the problem, sin θ and cos θ are given. Find the exactvalue of the indicated trigonometric function.

114) sin θ = 53, cos θ =

23

Find tan θ.

Find (i) the amplitude, (ii) the period, and (iii) the phaseshift.

115) y = - 12

sin(4x + 3π)

Write the equation of a sine function that has the givencharacteristics.

116) Amplitude: 4Period: 3π

Phase Shift: - π3

Find the area A. Round the answer to three decimalplaces.

117)

π5

10 m

Find the exact value of the expression if θ = 45°. Do notuse a calculator.

118) f(θ) = cos θ Find 11f(θ).

Use the even-odd properties to find the exact value ofthe expression. Do not use a calculator.

119) sec (-60°)

12

Find the exact value of the expression. Do not use acalculator.

120) sin π3

- cos π6

Use a calculator to find the value of the expressionrounded to two decimal places.

121) sin-1 35

Find the exact solution of the equation.

122) -sin-1(4x) = π4

Find the exact value, if any, of the composite function. Ifthere is no value, say it is "not defined". Do not use acalculator.

123) sin(sin-1 1.8)

Find the exact solution of the equation.124) 3 sin-1 x = π

125) -3 sin-1(2x) = π

Find the exact value of the expression.

126) cos sin-1 45

127) sin cos-1 - 35

128) tan(cos-1 1)

129) sec-1 -1

130) sin cos-1 - 22

Solve the equation on the interval 0 ≤ θ < 2π.131) 2 cos2 θ - 1 = 0

Solve the equation. Give a general formula for all thesolutions.

132) cos(2θ) = 22

Solve the equation on the interval 0 ≤ θ < 2π.

133) cot 2θ - π2

= 1

134) 1 + cos θ = 2 sin2 θ

Use a calculator to solve the equation on the interval 0 ≤θ < 2π. Round the answer to two decimal places.

135) csc θ = -5

Establish the identity.

136) 1 - cot2v1 + cot2v

+ 1 = 2 sin2v

137) (tan v + 1)2 + (tan v - 1)2 = 2 sec2v

138) 1 + csc xsec x

= cos x + cot x

139) 5 csc2 x + 4 csc x - 1

cot 2 x = 5 csc x - 1csc x - 1

140) 1 - sin tcos t

= cos t1 + sin t

13

Answer KeyTestname: FALL FINAL REVIEW 2017

1) (0, -14), (18.67, 0)ID: PCEGU6 1.1.7-5Objective: (1.1) Use a Graphing Utility to Approximate

Intercepts2) (-1.5 , -1)ID: PCEGU6 1.1.2-4Objective: (1.1) Use the Midpoint Formula

3) (h, k) = (-9, -2); r = 6ID: PCEGU6 1.5.3-4Objective: (1.5) Work with the General Form of the

Equation of a Circle4) NoID: PCEGU6 1.1.1-15Objective: (1.1) Use the Distance Formula

5) {5, 6}ID: PCEGU6 1.3.1-14Objective: (1.3) Solve Equations Using a Graphing Utility

6)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 1.5.2-7Objective: (1.5) Graph a Circle

7) y = -44x + 134ID: PCEGU6 1.4.5-15Objective: (1.4) Find the Equation of a Line Given Two

Points8) (0, -3), (-9, 0), (0, 3)ID: PCEGU6 1.2.1-3Objective: (1.2) Find Intercepts from an Equation

9) undefinedID: PCEGU6 1.4.1-9Objective: (1.4) Calculate and Interpret the Slope of a Line

10)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 1.2.3-2Objective: (1.2) Know How to Graph Key Equations

11) 2 5ID: PCEGU6 1.1.1-10Objective: (1.1) Use the Distance Formula

12) (0, -6.8), (-3.37, 0), (3.37, 0)ID: PCEGU6 1.1.7-7Objective: (1.1) Use a Graphing Utility to Approximate

Intercepts13) (h, k) = (-3, -6); r = 3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 1.5.3-2Objective: (1.5) Work with the General Form of the

Equation of a Circle

14) x2 + (y + 2)2 = 2ID: PCEGU6 1.5.1-8Objective: (1.5) Write the Standard Form of the Equation

of a Circle15) y = - 3400x + 17,000 ;

value after 2 years is $10,200 .00;ID: PCEGU6 1.4.5-10Objective: (1.4) Find the Equation of a Line Given Two

Points

14


16) slope = 47; y-intercept = - 1

7ID: PCEGU6 1.4.7-6Objective: (1.4) Identify the Slope and y-Intercept of a

Line from Its Equation

17) slope = - 35

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 1.4.8-5Objective: (1.4) Graph Lines Written in General Form

Using Intercepts18) y = 0.25 x + 0.45

ID: PCEGU6 1.4.5-14Objective: (1.4) Find the Equation of a Line Given Two

Points19)

x-5 5

y

5

-5

x-5 5

y

5

-5

y-axisID: PCEGU6 1.1.3-5Objective: (1.1) Graph Equations by Hand by Plotting

Points20) no solution

ID: PCEGU6 1.3.1-2Objective: (1.3) Solve Equations Using a Graphing Utility

21) y = x2 - 7ID: PCEGU6 2.5.1-3Objective: (2.5) Graph Functions Using Vertical and

Horizontal Shifts

22) local maximum at (0, 1)local minimum at (2, -3)ID: PCEGU6 2.3.6-8Objective: (2.3) Use Graphing Utility to Approximate

Local Maxima/Minima & Determine WhereFunc is Increasing/Decreasing

23)

x-5 5

y

5

-5

x-5 5

y

5

-5

ID: PCEGU6 2.5.2-8Objective: (2.5) Graph Functions Using Compressions and

Stretches24) negative

ID: PCEGU6 2.2.2-3Objective: (2.2) Obtain Information from or about the

Graph of a Function25) 14

ID: PCEGU6 2.3.7-6Objective: (2.3) Find the Average Rate of Change of a

Function26) even

ID: PCEGU6 2.3.2-8Objective: (2.3) Identify Even and Odd Functions from

the Equation27) none


Graph of a Function28) even

ID: PCEGU6 2.3.1-1Objective: (2.3) Determine Even and Odd Functions from

a Graph29) About 6 fish

ID: PCEGU6 2.1.2-20Objective: (2.1) Find the Value of a Function

30) (0, 4)ID: PCEGU6 2.4.2-10Objective: (2.4) Graph Piecewise-defined Functions

15


31) Absolute maximum: none; Absolute minimum: f(1)= 2ID: PCEGU6 2.3.5-3Objective: (2.3) Use a Graph to Locate the Absolute

Maximum and the Absolute Minimum32) A


Graph of a Function33) even


a Graph

34) - 23

ID: PCEGU6 2.1.2-2Objective: (2.1) Find the Value of a Function

35) AID: PCEGU6 2.5.1-2Objective: (2.5) Graph Functions Using Vertical and

Horizontal Shifts36) odd


a Graph

37) (f ∙ g)(x) = (5 - x)(x - 1); {x|1 ≤ x ≤ 5}ID: PCEGU6 2.1.4-9Objective: (2.1) Form the Sum, Difference, Product, and

Quotient of Two Functions38) odd


a Graph39) -60, 70, 100


Graph of a Function40) A

ID: PCEGU6 2.4.1-7Objective: (2.4) Graph the Functions Listed in the Library

of Functions41) F(c) = 1.8c + 32

ID: PCEGU6 3.1.4-8Objective: (3.1) Build Linear Models from Verbal

Descriptions

42) vertex (4, 1)intercept (0, 65)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 3.3.3-8Objective: (3.3) Graph a Quadratic Function Using Its

Vertex, Axis, and Intercepts43) (2, 4); x = 2

ID: PCEGU6 3.3.2-3Objective: (3.3) Identify the Vertex and Axis of Symmetry

of a Quadratic Function44) 3.2 s

ID: PCEGU6 3.5.1-25Objective: (3.5) Solve Inequalities Involving a Quadratic

Function45) 1958, 23.7 years old

ID: PCEGU6 3.4.1-8Objective: (3.4) Build Quadratic Models from Verbal

Descriptions

46) 11,552 ft2ID: PCEGU6 3.3.5-18Objective: (3.3) Find the Maximum or Minimum Value of

a Quadratic Function47) vertex (-6, -36)

intercepts (0, 0), (- 12, 0)

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40


Vertex, Axis, and Intercepts

16


48) f(x) = x2 + 4x + 3ID: PCEGU6 3.3.4-2Objective: (3.3) Find a Quadratic Function Given Its

Vertex and One Other Point49) Height increases as age increases.

ID: PCEGU6 3.2.1-8Objective: (3.2) Draw and Interpret Scatter Diagrams

50) increasing

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

ID: PCEGU6 3.1.3-1Objective: (3.1) Determine Whether a Linear Function Is

Increasing, Decreasing, or Constant51) 3 thousand automobiles

ID: PCEGU6 3.4.1-12Objective: (3.4) Build Quadratic Models from Verbal

Descriptions52)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 3.3.1-15Objective: (3.3) Graph a Quadratic Function Using

Transformations

53) -∞, 83


Function

54) vertex (1, 9)intercepts (4, 0), (- 2, 0), (0, 8)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10


Vertex, Axis, and Intercepts55) y = -2.12x + 12.78

x1 2 3 4 5

y14

12

10

8

6

4

2

x1 2 3 4 5

y14

12

10

8

6

4

2

ID: PCEGU6 3.2.1-4Objective: (3.2) Draw and Interpret Scatter Diagrams

56) y = 1.02x + 11.7ID: PCEGU6 3.2.3-15Objective: (3.2) Use a Graphing Utility to Find the Line of

Best Fit57) 5 < t < 6


Function58) 0

ID: PCEGU6 3.1.2-4Objective: (3.1) Use Average Rate of Change to Identify

Linear Functions

17


59)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

ID: PCEGU6 3.3.1-12Objective: (3.3) Graph a Quadratic Function Using

Transformations60) -1

ID: PCEGU6 3.1.2-3Objective: (3.1) Use Average Rate of Change to Identify

Linear Functions61) x = 3

ID: PCEGU6 4.4.2-14Objective: (4.4) Find the Vertical Asymptotes of a Rational

Function

62) ± 16, ± 13, ± 12, ± 23, ± 1, ± 2

ID: PCEGU6 4.2.2-2Objective: (4.2) Use the Rational Zeros Theorem to List

the Potential Rational Zeros of a PolynomialFunction

63) -4, 4; f(x) = (x - 4)(x + 4)(x2 + 4)ID: PCEGU6 4.2.3-1Objective: (4.2) Find the Real Zeros of a Polynomial

Function64)

x-5 5

y

5

-5

x-5 5

y

5

-5

ID: PCEGU6 4.4.4-2Objective: (4.4) Demonstrate Additional Understanding

and Skills

65) No; x is raised to non-integer powerID: PCEGU6 4.1.1-12Objective: (4.1) Identify Polynomial Functions and Their

Degree66) {x|x > 9}; (9 , ∞)

ID: PCEGU6 4.6.1-20Objective: (4.6) Solve Polynomial Inequalities

Algebraically and Graphically

67) 0, 361331

ID: PCEGU6 4.5.1-14Objective: (4.5) Analyze the Graph of a Rational Function

68) 1, 1; f(x) = (x - 1)2(3x2 + 1)ID: PCEGU6 4.2.3-6Objective: (4.2) Find the Real Zeros of a Polynomial

Function

69) 0, 712


70) no horizontal asymptotesID: PCEGU6 4.4.3-2Objective: (4.4) Find the Horizontal or Oblique

Asymptotes of a Rational Function71) (-∞, -8) ∪ [-1, 4) ∪ [11, ∞)

ID: PCEGU6 4.6.2-16Objective: (4.6) Solve Rational Inequalities Algebraically

and Graphically72) 0, multiplicity 2, touches x-axis;

5 , multiplicity 1, crosses x-axis;- 5, multiplicity 1, crosses x-axisID: PCEGU6 4.1.3-14Objective: (4.1) Identify the Real Zeros of a Polynomial

Function and Their Multiplicity

73) 23; f(x) = (3x - 2)(x2 + 2)

ID: PCEGU6 4.2.3-4Objective: (4.2) Find the Real Zeros of a Polynomial

Function74) x-intercepts: -6, -4, 4; y-intercept: -96

ID: PCEGU6 4.1.4-3Objective: (4.1) Analyze the Graph of a Polynomial

Function75) no oblique asymptote

ID: PCEGU6 4.4.3-17Objective: (4.4) Find the Horizontal or Oblique

Asymptotes of a Rational Function

18


76) x = 0ID: PCEGU6 4.4.2-16Objective: (4.4) Find the Vertical Asymptotes of a Rational

Function77) x-intercepts: 0, 2, -2; y-intercept: 0

ID: PCEGU6 4.2.3-17Objective: (4.2) Find the Real Zeros of a Polynomial

Function78) (0, 0)


79) No; x is raised to a negative powerID: PCEGU6 4.1.1-6Objective: (4.1) Identify Polynomial Functions and Their

Degree80) (-3, 2) ∪ (4, ∞)

ID: PCEGU6 4.6.1-3Objective: (4.6) Solve Polynomial Inequalities

Algebraically and Graphically81) {x x ≠ -11}

ID: PCEGU6 5.1.2-2Objective: (5.1) Find the Domain of a Composite Function

82) f(t) = 200,000e0.238tID: PCEGU6 5.8.1-3Objective: (5.8) Find Equations of Populations That Obey

the Law of Uninhibited Growth83) 3.00 min

ID: PCEGU6 5.4.5-23Objective: (5.4) Solve Logarithmic Equations

84) 298


85) {-2}ID: PCEGU6 5.3.4-8Objective: (5.3) Solve Exponential Equations

86) {5}, (5 , 129)ID: PCEGU6 5.6.1-16Objective: (5.6) Solve Logarithmic Equations

87) {-3}ID: PCEGU6 5.3.4-9Objective: (5.3) Solve Exponential Equations

88) {27}ID: PCEGU6 5.6.1-7Objective: (5.6) Solve Logarithmic Equations

89) log(x - 1) + log(x2 + x + 1) - 3 log xID: PCEGU6 5.5.2-13Objective: (5.5) Write a Logarithmic Expression as a Sum

or Difference of Logarithms

90) 24.9 ftID: PCEGU6 5.4.2-17Objective: (5.4) Evaluate Logarithmic Expressions

91) - 129

ID: PCEGU6 5.1.1-8Objective: (5.1) Form a Composite Function

92)

x-4 -2 2 4 6

y6

4

2

-2

-4

-6

x-4 -2 2 4 6

y6

4

2

-2

-4

-6

domain of f: (-∞, ∞); range of f:(2, ∞) horizontal asymptote: y = 2ID: PCEGU6 5.3.2-8Objective: (5.3) Graph Exponential Functions

93) 9.1 lb/in.2ID: PCEGU6 5.3.3-15Objective: (5.3) Define the Number e

94) ln (x - 8)7

x2

ID: PCEGU6 5.5.3-5Objective: (5.5) Write a Logarithmic Expression as a

Single Logarithm95) A

ID: PCEGU6 5.4.4-1Objective: (5.4) Graph Logarithmic Functions

96) log x(x + 13)9

ID: PCEGU6 5.5.3-10Objective: (5.5) Write a Logarithmic Expression as a

Single Logarithm97) {121, -121}


98) 6 yrID: PCEGU6 5.7.4-7Objective: (5.7) Determine the Rate of Interest or Time

Required to Double a Lump Sum of Money

19


99) Yes, yesID: PCEGU6 5.1.1-24Objective: (5.1) Form a Composite Function

100) 6 minutesID: PCEGU6 5.8.3-8Objective: (5.8) Use Newton's Law of Cooling

101) 25ID: PCEGU6 6.6.1-14Objective: (6.6) Graph Sinusoidal Functions of the Form y

= A sin (ωx - φ) + B102) amplitude = 0.65, period = 5, respiratory cycle = 5

seconds

a = 0.65sin 2π5t

t5 10

a

0.65

-0.65

t5 10

a

0.65

-0.65

ID: PCEGU6 6.4.3-16Objective: (6.4) Determine the Amplitude and Period of

Sinusoidal Functions

103) 29π60ID: PCEGU6 6.1.3-5Objective: (6.1) Convert from Degrees to Radians and

from Radians to Degrees

104) y = -3 cos 13x

ID: PCEGU6 6.4.5-13Objective: (6.4) Find an Equation for a Sinusoidal Graph

105) integral multiples of π (180°)ID: PCEGU6 6.3.1-3Objective: (6.3) Determine the Domain and the Range of

the Trigonometric Functions

106) π units to the rightID: PCEGU6 6.6.1-19Objective: (6.6) Graph Sinusoidal Functions of the Form y

= A sin (ωx - φ) + B

107) 2455 cm2ID: PCEGU6 6.1.4-7Objective: (6.1) Find the Area of a Sector of a Circle

108) 2 33

ID: PCEGU6 6.3.6-7Objective: (6.3) Use Even-Odd Properties to Find the

Exact Values of the Trigonometric Functions109) -210°

ID: PCEGU6 6.1.3-8Objective: (6.1) Convert from Degrees to Radians and

from Radians to Degrees110) 4.94 ft

ID: PCEGU6 6.5.2-9Objective: (6.5) Graph Functions of the Form y = A csc

(ωx) + B and y = A sec (ωx) + B111) 1

ID: PCEGU6 6.2.3-2Objective: (6.2) Find the Exact Values of the Trigonometric

Functions of pi/4 = 45°112) 1

ID: PCEGU6 6.3.4-5Objective: (6.3) Find the Values of the Trigonometric

Functions Using Fundamental Identities113) 3

ID: PCEGU6 6.6.1-3Objective: (6.6) Graph Sinusoidal Functions of the Form y


114) 52

ID: PCEGU6 6.3.4-1Objective: (6.3) Find the Values of the Trigonometric

Functions Using Fundamental Identities

115) (i) 12

(ii) π2

(iii) - 3π4



116) y = 4 sin 23x + 29π



20


117) 31.416 m2ID: PCEGU6 6.1.4-10Objective: (6.1) Find the Area of a Sector of a Circle

118) 11 22


Functions of pi/4 = 45°119) 2

ID: PCEGU6 6.3.6-3Objective: (6.3) Use Even-Odd Properties to Find the

Exact Values of the Trigonometric Functions120) 0


Functions of pi/6 = 30° and pi/3 = 60°121) 0.64

ID: PCEGU6 7.1.2-4Objective: (7.1) Find an Approximate Value of the Inverse

Sine, Cosine, and Tangent Functions

122) x = - 28

ID: PCEGU6 7.1.5-8Objective: (7.1) Solve Equations Involving Inverse

Trigonometric Functions123) not defined

ID: PCEGU6 7.1.3-16Objective: (7.1) Use Properties of Inverse Functions to

Find Exact Values of Certain CompositeFunctions

124) x = 32


Trigonometric Functions

125) x = - 34


Trigonometric Functions

126) 35ID: PCEGU6 7.2.1-22Objective: (7.2) Find the Exact Value of Expressions

Involving the Inverse Sine, Cosine, andTangent Functions





129) πID: PCEGU6 7.2.2-3Objective: (7.2) Define the Inverse Secant, Cosecant, and

Cotangent Functions

130) 22

ID: PCEGU6 7.2.1-4Objective: (7.2) Find the Exact Value of Expressions


131) π4, 3π4, 5π4, 7π4

ID: PCEGU6 7.3.1-7Objective: (7.3) Solve Equations Involving a Single

Trigonometric Function

132) θ|θ = π8

+ kπ, θ = 7π8

+ kπ

ID: PCEGU6 7.3.1-34Objective: (7.3) Solve Equations Involving a Single


133) 3π8, 7π8, 11π8, and 15π

8ID: PCEGU6 7.3.1-25Objective: (7.3) Solve Equations Involving a Single


134) π3, π, 5π

3ID: PCEGU6 7.3.4-10Objective: (7.3) Solve Trigonometric Equations Using

Fundamental Identities135) 6.08 , 3.34

ID: PCEGU6 7.3.2-7Objective: (7.3) Solve Trigonometric Equations Using a

Calculator

21


136) 1 - cot2v1 + cot2v

+ 1 = 1 - cot2v csc2v

+ 1 = 1 csc2v

- cot2v

csc2v + 1

= sin2v -

cos2vsin2v

1sin2v

+ 1

= sin2v - cos2v + (sin2v + cos2v) = 2 sin2vID: PCEGU6 7.4.2-25Objective: (7.4) Establish Identities

137) (tan v + 1)2 + (tan v - 1)2 = tan2v + 2 tan v + 1 + tan2v- 2 tan v + 1 = 2(tan2v + 1) = 2 sec2vID: PCEGU6 7.4.2-11Objective: (7.4) Establish Identities

138) 1 + csc xsec x

= cos x 1 + 1sin x

= cos x (sin x + 1)sinx

=

cos x sin xsin x

+ cos xsin x

= cos x + cot x.

ID: PCEGU6 7.4.2-37Objective: (7.4) Establish Identities

139) 5 csc2 x + 4 csc x - 1

cot2 x = (5 csc x - 1) (csc x + 1)

csc2 x - 1 =

(5 csc x - 1) (csc x + 1)(csc x - 1) (csc x + 1)

= 5 csc x - 1csc x - 1

.


140) 1 - sin tcos t

= 1 + sin t1 + sin t

1 - sin tcos t

= cos 2 tcos t (1 + sin t)

=

cos t1 + sin t

.


22

chapters 1 6 and chapter 7 sections 1 4 short …...the graph shows the depreciation of the...

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