Free Printable IM3 Fall 2023 Exam Review (Units 1 & 2)

1.

Are the blue and red graphs inverse functions?

a)

Yes, the functions reflect over y = x

b)

No, they do not reflect over the x - axis.

c)

No way to tell from a graph

2.

Are these inverse functions?

a)

no

b)

yes

c)

no way to tell

3.

What is the inverse of the given relation? {(1, 2) (3, 8) (-3, 6)}

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

4.

Which is the inverse of the table?

a)

b)

c)

d)

5.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

6.

a)

Inverse Functions

b)

Not Inverse Functions

7.

What is the inverse of the function $\frac{x+3}{3}$

a)

$9x$

b)

$3x-3$

c)

$x+1$

d)

$3x+3$

8.

Find the inverse for $f\left(x\right)=x^2-1$

a)

$-x+1$

b)

$2x+1$

c)

$\sqrt{x}+1$

d)

$\sqrt{x+1}$

9.

Find the inverse of $f\left(x\right)=\sqrt{x}+8$

a)

$f^{-1}\left(x\right)=x^2+8$

b)

$f^{-1}\left(x\right)=x^2-8$

c)

$f^{-1}\left(x\right)=\left(x+8\right)^2$

d)

$f^{-1}\left(x\right)=\left(x-8\right)^2$

10.

Which is the inverse of the table?

a)

b)

c)

d)

11.

Which graph is the inverse of the graph shown?

a)

b)

c)

d)

12.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

13.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

14.

Are the following inverses of each other?

a)

True

b)

False

15.

In an inverse function, the _____ and _______ are switched from the original

a)

f(x) and g(x)

b)

input and output

c)

positives and negatives

d)

slope and intercept

16.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

17.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

18.

What is the inverse of the function f(x)=4-2x

a)

f⁻¹(x) = 2x-½

b)

f⁻¹(x) = 2x+½

c)

f⁻¹(x) = 2+½x

d)

f⁻¹(x) = 2-½x

19.

Is this function invertible? In other words will its inverse also be a function?

a)

No

b)

Yes

c)

No way to tell

20.

Is this function invertible? In other words will its inverse also be a function?

a)

Yes

b)

No

c)

No way to tell

21.

Match the following functions to their inverses

a)

$f\left(x\right)=2x-7$

1.

$f^{-1}\left(x\right)=\frac{x+7}{2}$

b)

$f\left(x\right)=7x+2$

2.

$f^{-1}\left(x\right)=\frac{x-2}{7}$

c)

$f\left(x\right)=\sqrt[]{x-7}+2$

3.

$f^{-1}\left(x\right)=\left(x-2\right)^2+7$

d)

$f\left(x\right)=\left(x+2\right)^2-7$

4.

$f^{-1}\left(x\right)=\sqrt[]{x+7}-2$

22.

What is the DOMAIN of the function?

a)

[-3, infinity)

b)

[0, infinity)

c)

[3, inifinity)

d)

(-infinity, 0}

23.

To which intervals could we restrict the domain of f(x) to make it an invertible function? Choose all answers that apply.

a)

-4 ≤ x < 0

b)

0 < x ≤ 4

c)

4 ≤ x < 8

d)

none of the above

24.

To which intervals could we restrict the domain of f(x) to make it an invertible function? Choose all answers that apply.

a)

-1 < x < 1

b)

-2 < x < 0

c)

0 < x < 1

d)

none of the above

25.

To which intervals could we restrict the domain of f(x) to make it an invertible function? Choose all answers that apply.

a)

0 ≤ x ≤ 4

b)

-2 ≤ x ≤ 2

c)

0 ≤ x ≤ 2

d)

none of the above

26.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

27.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

28.

Evaluate the log:
log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

29.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

30.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

31.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

32.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

33.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

34.

Expand

a)

A

b)

B

c)

C

d)

D

35.

Expand

a)

A

b)

B

c)

C

d)

D

36.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

37.

Expand
$\log_2\ \left(\frac{8x^3}{2y}\right)$

a)

$2+3\log_2x-\log_2y$

b)

$4+3\log_2x-\log_2y$

c)

$3\log_2x-\log_2y$

d)

$3\log_2x-3\log_2y$

38.

Condense $15\ \log_5a\ +3\ \log_5b$

a)

$15\log_5ab$

b)

$\log_5\left(a^{15}b^3\right)$

c)

$\log_5\left(b^{15}a^3\right)$

d)

$45\log_5\left(ab\right)$

39.

Condense into a single log:

\log_320-\log_35

a)

$\log_315$

b)

$\log_34$

c)

$\log_3100$

d)

$\log_3\frac{1}{4}$

40.

Write equation in exponential form.

$\log_3\frac{1}{27}=-3$

a)

$-3^3\ =\ \frac{1}{27}$

b)

$\frac{1}{27}^3=-3$

c)

$3^{\frac{1}{27}}=-3$

d)

$3^{-3}=\frac{1}{27}$

41.

Expand

a)

A

b)

B

c)

C

d)

D

42.

Condense

a)

A

b)

B

c)

C

d)

D

43.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

44.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

45.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: All Real Numbers
Range: y>0

b)

Domain: All Real Numbers
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

46.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

47.

What is the Vertical Asymptote?

a)

x=5

b)

x=0

c)

y=0

d)

x=1

48.

What is the Domain?

a)

x > 0

b)

All Real Numbers

c)

x > 1

d)

x < 1

49.

What is the Range?

a)

y > 0

b)

All Real Numbers

c)

y > 1

d)

y < 1

50.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

51.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

52.

What is the Domain?

a)

x > -3

b)

x > 5

c)

x > 3

d)

x > -5

53.

What is the range of this graph?

a)

All Real Numbers

b)

y > 1

c)

y > -1

d)

y > 5

54.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

55.

What's the corresponding graph of

a)

b)

c)

d)

56.

What's the corresponding graph of

a)

b)

c)

d)

57.

f(x)=log₅(x+4) - 2

Describe the transformation

a)

translation 4 units to the right, 2 units down

b)

translation 4 units to the left, 2 units down

c)

translation 4 units to the up, 2 units right

d)

translation 4 units to the up, 2 units left

58.

Rewrite the following exponent as a logarithm $e^4=x$ .

a)

$e^x=4$

b)

$\ln e=4$

c)

$\ln x=4$

d)

$\log4=e$

59.

Rewrite the logarithmic equation in exponential form $\ln3=x$ .

a)

$x=0$

b)

$e^3=x$

c)

$x=\frac{1}{3}$

d)

$e^x=3$

60.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

61.

Which of the following is the value of x given;
7e^(3x-5) = 49

a)

x = 2.315

b)

x = 0.681

c)

x = 2.964

d)

No Solution

62.

Simplify the following: $e^5\cdot e^7$

a)

$e^{12}$

b)

$e^2$

c)

$e^7$

d)

$e^{-2}$

63.

Condense: $3\ln x\ +\ 8\ln y$

a)

$\ln\left(\frac{x^3}{y^8}\right)$

b)

$\ln\left(x^3y^8\right)$

c)

$24\ln\left(xy\right)$

d)

$11\ln\left(xy\right)$

64.

Heather invested $8,000 in a 4-year Certificate of Deposit (CD) that pays 4.1% interest compounded annually. What is the value of the CD at the end of the 4 years?

a)

$9,394.92

b)

$9,312.00

c)

$1394.00

d)

$1312.00

65.

Zach's parents put $1,500 in his bank account for college tuition. At an interest rate of 8.25% compounded semi-annually, what will be the balance after 18 years?

a)

$6,273.50

b)

$6,314.08

c)

$6,385.72

d)

$6,427.94

66.

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

67.

What is the FIRST step to solving this equation?
$-5\cdot10^{4x}=60$

a)

take the LOG of both sides

b)

add 5 to both sides

c)

divide by -5 on both sides

d)

divide by 4 on both sides

68.

In order to cancel out the $10^{power}$ in an equation, you would need to take the ___________ of both sides.

a)

LOG

b)

LN

c)

e

d)

divide by 10

69.

In order to cancel out the $e^{power}$ in an equation, you would need to take the ___________ of both sides.

a)

LOG

b)

LN

c)

e

d)

divide by e

70.

What is the FIRST step in solving this equation?

4\cdot10^{2x}=40,000

a)

divide by 4

b)

divide by 10

c)

subtract 4

d)

take the LN of both sides

71.

$10^x=39$