Precalculus Chapter 1 Functions and Their Graphs Final Exam Review

1) Given the segment with endpoints ( – 2, 5) and (6, 0),

find the coordinates of the midpoint of the segment

and the length of the segment.

2) Graph a) b) c)

3) Sketch the graph of

4) Write the standard for the equation of the circle in the given picture

5) Evaluate at f(7), f(–5), and f(x – 9)

6) Find the domain of the rational functions

a) b)

7) Find the real zeros of each function. Approximate any relative minimums or maximums to two decimal places. Approximate over which intervals the function is increasing, decreasing or constant. Then determine whether the functions are symmetric to the x-axis, y-axis, or the origin. Then determine if they are even, odd, or neither.

a)

b)

c)

8) Determine whether y is a function of x. Then determine whether the inverse is a function.

a) b)

c)

9) Identify the parent function. Then describe the

sequence of transformations from f to h

a)

b)

c)

10) If and , find

a)

11) Find the inverse of

12) Find a regression line for the data below. Let x = 5 correspond to 1995. Identify the correlation coefficient and state whether it’s a good fit. Then use the model to estimate the sales in 2008.

Year 1995 1996 1997 1998 1999 2000 2001

Sales 3000 3500 3900 4480 5100 5850 6725

13) The cost of making a wooden box varies jointly as

the height of the box and the square of the width of the

box. A box of height 16 in and width 6 in costs $28.80.

How much would a box of height 14 in and width 8 in

cost?

Precalculus Chapter 2 Polynomial and Rational Functions Final Exam Review

1) Sketch the graph of . Identify the vertex, axis of symmetry, and x-intercepts

2) Use the Intermediate Value Theorem and the table of your calculator to find intervals one unit in length in which

is guaranteed to have a zero.

3) Jason jumped off of a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function , where t is the time in seconds and h is the height in feet.

a) What was the maximum height he reached?

b) How long did it take for him to reach his maximum height?

c) How many seconds did it take for him to hit the ocean?

4) Find an equation in the form for the parabola that has a vertex of (3, –6) and goes through the

point (0, 3).

5) Determine the right and left-hand behavior of the graph of the function without graphing.

6) Divide using synthetic division

7) Perform the given operation and write the result in standard form:

a) b)

8) Write the quotient in standard form:

9) Write a polynomial function with real coefficients that has zeros of 0, 2, 3i, and –3i

10) Find all the zeros of the function

a) b)

11) Identify the horizontal and vertical asymptotes of the function . Then sketch a graph.

Chapter 3 Review Exponential and Logarithmic Functions

1) Graph the function g(x) = log2x and its inverse on the same grid. Then state the domain and range of each function.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

Use the graph of f to describe the transformation that

yields the graph g

2)

3)

Evaluate without a calculator:

Use the properties of logarithms to expand the

expression.

Formulas:

tn

n

rPA 1

A Per t

Condense the expression to a single logarithm

Solve the equation algebraically. Approximate your

result to three decimal places.

17)

21)

Applications:

23) Find the amount of money in an account after 10

years if the initial investment was $3500 at 6.5%

a) Compounded monthly

b) Compounded continuously

24) How long would it take $7550 to triple if it’s in an

account compounded continuously at 7.25% interest?

25) The population of South Carolina (in millions) from

1990 through 2003 can be modeled by

where t represents the year with

t = 0 corresponding to 1990. According to this model,

when will the population reach 4.5 million?

26) The antler spread a (in inches) and shoulder height

h (in inches) of an adult male American elk are related

by the model .

Approximate the shoulder height of a male American

elk with an antler spread of 55 inches.

Chapter 9 Review: Sequences and Series

Determine the common difference, and find the next four terms of the arithmetic sequence. 1. -1.1, 0.6, 2.3, …

Determine the common ratio and find the next three terms of the geometric sequence. 2. -4, -3, -9/4, …

Find an explicit formula for the nth term of each arithmetic sequence. 3. 9, 13, 17, …

Write an explicit formula for the nth term of the geometric sequence. 4. 2, 10, 50, …

Find the specified value for the arithmetic sequence with the given characteristics. 5. If a1 = -27 and d = 3, find a24 .

Find the specified term for the geometric sequence with the given characteristics. 6. a5 for 20, 2, 0.2, …

Find the indicated sum of each arithmetic series 7. S13 of -5 + 1 + 7 + … + 67 if a1 = -5

8. 62nd partial sum of -23 + (-21.5) + (-20) + …

9. Find the sum Find the indicated sum of each geometric series 10. first eight terms of – 3/4 + −9/20 + −27/100 + …

11. If possible, find the sum of each infinite geometric series. 12. 10 + 5 + 2.5 + …

13. Application. 14. DESIGN Wakefield Auditorium has 26 rows.

The first row has 22 seats. The number of seats in each row increases by 4 as you move to the back of the auditorium. a. How many seats are in the last row?

b. What is the total seating capacity?

15. WORK The first-year salary of an employee is

$34,500. Each year thereafter, her annual salary increases by $750. a. What will her salary be her 10th year?

b. What will her total earnings be for 25 years? 16. POPULATION A city is growing at a rate of

5.2% per year. The first year of a census finds the population at 100,000 people. Assuming this growth rate remains constant, estimate the population in the fifth year of the census.

Equations:

an = a1 + (n – 1)d an = a1 r n – 1

nn aan

S 12

r

raS

n

n1

11

1

1

1

i

i r

aa