Please do the following problems as a review for your midterm. Look over all note and

homework for extra problems to review. Remember to bring your graphing calculator and a

pencil. The exam consists of Unit 0 (sections P.1, P.3, P.5); Unit 1 (sections 1.2 – 1.6); Unit 2

(sections 2.2 – 2.6, 2.8); Unit 3 (sections 3.1 – 3.6). There will be calculator and non-

calculator parts on the exam.

Your exam is on _____________________________ at _______________________.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Rewrite each as an inequality:

1) 2) ( ,7)

Solve each inequality – graph the solution set – write your final answer in interval notation.

3) 4 2 7x x 4) 5 3 1 7x

Solve by factoring:

5) 2 16 48 0x x 6) x² = 49

7) 32 50 0x x 8)

22 3 5 0x x

Solve by Quadratic Formula: 9) 3x² + 2x – 5 = 0 10) x² - 5x = - 8 Indicate if the functions are even, odd, or neither.

11) f(x) = 5x6 + 3x

2 – 6 12) f(x) = -4x

3 + 2x 13) f(x) = 2x + 1

14) Find the domain of each function:

(a) 9

)(2

x

xxf (b)

2

3)(

2

x

xxf

(c) xxf 2)( (d) ( ) 3 2f x x

15) For the following functions, find:

gf , gf , gf , g

f, (f ∙ g)(4),

g

f(-2), (f o g)(x), (g o f)(2)

(a) 13)(;2)( xxgxxf (b) xxgxxxf 3)(;13)( 2

16) Graph (on graph paper):

(a)

1,23

1,32)(

xx

xxxf (b)

2,32

2,3)(

xx

xxxf

17) For the following graph, determine the following:

(a) Domain, Range

(b) Intervals of increasing and

decreasing

(c) Min/Max

(d) Intercepts

18) Find the resulting function after all of the transformations below are applied to the

graph of xxf )( :

(a) Shift up 2 units (b) Reflect x-axis (c) Shift up 2 units

Reflect x-axis Shift right 3 units Reflect y-axis

Reflect y-axis Shift down 2 units Shift left 3 units

19) Graph each function (on graph paper):

(a) 1)( 2 xxf (b) 3( ) 4f x x

(c) 1)3()( 3 xxf (d) 32)( xxf

(e) 24

1)(

xxf (f)

51

( )2

x

f x

(g) 32)( 2 xxf (h) 5( ) 1xf x e

(i) 53)( xxf (j) 41)( xxf

20) Determine the inverse and is the inverse a function?

(a) { (2, 3), (5, -6) (0, 3) } (b) 24)( xxf (c) 3

( ) 3 5f x x

21) Form a polynomial with the given zeros:

(a) Zeros: -1, 1, 3 (b) Zeros: -2, 2, 3

(c) Zeros: -4, 0, 2 (d) Zeros: 2 (mult 2), 3, 5

22) Solve each polynomial inequality (set up chart and testing values):

(a) 1272 xx (b) 043 24 xx

23) Determine whether g(x) is a factor of f(x) using synthetic division.

(a) 1)(;438)( 23 xxgxxxxf

24) Using the remainder theorem, find the remainder and is the binomial a factor?

(a) 2)(;5582)( 23 xxgxxxxf

25) Find the zeros of each polynomial function (use calc to find first or second real zero,

if necessary, then factor or use quadratic formula to find the rest):

(a) 863 23 xxx =0 (b) 81023 xxx =0

(c) 202094 234 xxxx =0 (d) 1812116 234 xxxx =0

(e) 082 24 xx (f) 012823 xxx

26) For the following, determine the degree of each polynomial, the zeros, and whether

each zero crosses or touches the x-axis, and find the end behavior.

(a) )4)(2()( xxxxf (b) )4)(23()1()( 22 xxxxf

27) Find the x-int, y-int, horizontal, vertical, and slant asymptotes of the functions below.

(a) 17

723

3

x

xx (b)

1

2832

2

x

xxx

(c) 5

53 2

x

x (d)

9

83

x

x

28) Solve each equation:

(a) 42 12 x (b) 2

18 22

xx

(c) 27 81x (d) 35 7x

(e) ln(3 1) 3x (f) 5log 7 2x

(g) 3 3log ( 8) log 2x x (h) log( 4) log log2x x

29) Evaluate the logs.

(a) 2

1log

16 (b) 27log 9

30) Find the domain. Remember to find critical values, test values and t/f.

2

8log 13 30f x x x

31) Rewrite in expanded log form.

a) 2

4 5log xy

b) y

x

5ln

9

c) 8

625log

z

y

32) Rewrite as a single log.

a) xxx log4)3log(log2

b) )loglog3(100log2

1yx

c) 2 2

2 2log 16 log 6 8x x x

d) 3

7 7 7

19log 4log log 16

2k k

State the equation you will use and then solve the problem. Round to the fourth place

(if necessary) while doing any calculations during the problem. Then solve according

to the directions given in the problem.

33. The initial amount of a substance is 50mg. If its half-life is 6 days, how much substance

is left after 26 days? Round to the hundredth.

34. Devin deposited $2000 into her account which compounds quarterly. Find the amount in

her account after 6 years if the rate is 7.3%. Round to the nearest cent.

35. Kevin bought a $200 poster of Chuck Norris which depreciates 1.5% per year. If the

poster is worth $155, how long did it take to depreciate? Round to the nearest year.

36. Chris invested $250 into an account at 6% compounded annually. How long does it take

for his account to be $1000? Round to the nearest year.

37. Grace invested $630 into her bank account compounded continuously for seven years.

What is the rate that will produce her balance to be $950? Round the fourth place and

then write as a percent.

38. Annie invests $20,000 at Bank of America at 8.75% annual interest compounded

monthly. What is the equivalent APY? Round to the fourth place and then put into

percent.

39. Which investment would you choose? Plan A with 9.6% compounded quarterly or Plan

B with 8.8% compounded daily? Show why.

40. At the end of each quarter year, Scott deposits $250 into an account. If his investments

earn 5.8% annual interest compounded quarterly, what will the value of Scott’s annuity

be in 12 yrs? Round to the nearest cent.

41. Steffi wants to purchase a signed copy CD of Justin Bieber for $2,500 and needs a loan.

If she has $300 as a down payment, what would her monthly payments be for a 3 yr loan

if the annual rate is 2.5%?

42. On 11/1/11 there were two earthquakes. One in Southern California measuring a 4.1

and one in Revilla Gigedo Islands (part of Mexico in Pacific Ocean) measuring a 6.3.

Find the order of magnitude, and how many times more severe the Revilla Gigedo

Islands than Southern California.

Round to the hundredth.

43. Coca-Cola has a pH level of 3.4 and Chocolate Milk has a pH level of 6.74.

a) What are their hydrogen-ion concentrations? Round to the hundredth.

b) Find the orders of magnitude and how many times greater the hydrogen-ion

concentration of the coke is to the chocolate milk. Round to the hundredth.

44. A cake is removed from an oven at 220℉ and cools to 150℉ after 35 minutes in a room

at 75℉. When will it cool to 95℉? Round to the hundredth.