Free Printable Final Exam Review 2023

1.

a)

14

b)

-14

c)

6

d)

-6

2.

a)

2

b)

-2

c)

4

d)

-4

3.

What transformations are taking place in the function $f\left(x\right)=-\sqrt{x+9}$

a)

Reflect across the x-axis, shift left 9 units

b)

Reflect across the x-axis, shift right 9 units

c)

reflect across the y-axis, shift left 9 units

d)

reflect across the y-axis, shift right 9 units

4.

How can you verify your intercepts on the test?

a)

Enter equation into the graphing calculator and look at your graph or the table.

b)

No way to check, you know or you don't.

5.

Enter $f\left(x\right)=-\sqrt{x-5}+1$ into your calculator. Determine the min and max values on the interval [6, 21] by looking at the table.

a)

$\min=-3;\ \max=0$

b)

$\min=0;\ \max=-3$

c)

$\min=-4;\ \max\ =\ 1$

6.

What is the domain of the function in this graph?

a)

x ≤ 3

b)

x ≥ 3

c)

x ≤ 0

d)

x ≥ 0

7.

What is the domain?

a)

All Real Numbers

b)

$\left[1,\ \infty\right]$

c)

$\left(\infty,\ 1\right)$

d)

$\left(1,\infty\right)$

8.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

9.

Determine the inverse of $f\left(x\right)=7^x$

a)

$f^{-1}\left(x\right)=\log_7x$

b)

$f^{-1}\left(x\right)=\log_x7$

c)

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

10.

Determine the inverse of $f\left(x\right)=\log_4x$

a)

$f^{-1}\left(x\right)=x^4$

b)

$f^{-1}\left(x\right)=4^x$

c)

$f^{-1}\left(x\right)=4x$

11.

What is the range of the graph?

a)

$\left(\infty,\ -2\right)$

b)

$\left(-2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)$

12.

Which function has a domain of x = all real numbers?

a)

$f\left(x\right)=3e^{\left(x+4\right)}$

b)

$f\left(x\right)=-2\log\left(x-4\right)$

13.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

14.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

15.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

16.

Factor

3v² - 4v - 7

a)

(3v - 7)(v + 1)

b)

3(v - 7)(v - 1)

c)

(3v + 1)(v - 9)

d)

(3v + 1)(v - 10)

17.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

18.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

19.

Factor by Grouping:

2x³+ 5x² + 6x + 15

a)

(x² + 3) (2x + 5)

b)

(x² - 3) (2x - 5)

c)

(2x² - 3) (x - 5)

d)

(2x² + 3) (x + 5)

20.

$\left(a^3+b^3\right)=$

Complete the formula

a)

$\left(a+b\right)\left(a^2+ab+b^2\right)$

b)

$\left(a+b\right)\left(a^2-ab+b^2\right)$

c)

$\left(a-b\right)\left(a^2-ab+b^2\right)$

21.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

22.

Which equation will help you solve for x?
$\log_6\left(3x+2\right)=\log_6\left(5x-8\right)$

a)

$3x+2+5x-8=0$

b)

$6^{\left(5x-8\right)}=3x+2$

c)

$3x+2=5x-8$

d)

No equation will help you

23.

Which equation will help you solve for x?
$\log\left(3x+25\right)=2$

a)

$3x+25=2$

b)

$2^2=3x+25$

c)

No equation will help you

d)

$10^2=3x+25$

24.

Which equation will help you solve for x?

\log_2\left(x-4\right)=6

a)

x - 4 = 6²

b)

6₂ = x - 4

c)

2^(x-4) = 6

d)

2⁶ = x - 4

25.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

26.

Solve the equation:
$\log_2\left(7x-4\right)=\log_2\left(3+8x\right)$

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

27.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

28.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

29.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

30.

To solve 8 = 2^5x+7, you would need to re-write 8 as what?

a)

$2^4$

b)

$4^2$

c)

$2^3$

31.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

32.

What is an inverse relation?

a)

for ordered pairs (x, y) , the set of all ordered pairs (y, x)

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

33.

Describe the transformations of f(x)= -log₂(x+1)

a)

left one & y-axis reflection

b)

right one & y-axis reflection

c)

left one & x-axis reflection

d)

right one & x-axis reflection

34.

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

35.

What is the relationship between
f(x) = log₅(x)
and
g(x) = 5^x?

a)

No Relationship

b)

Inverses

c)

Same Function

36.

If $f\left(x\right)=3^x$ , then its inverse is $f^{-1}\left(x\right)\ =\ \log_3x$ If f(3) = 27, then what is $f^{-1}\left(27\right)$ ?

a)

-3

b)

3

c)

-27

d)

1/3

37.

Determine the minimum and maximum of $f\left(x\right)=-2\log_2x$ on the interval [4,8] (Hint: Look at the table.)

a)

minimum = 4
maximum = 8

b)

minimum = 2
maximum = 3

c)

minimum = -6
maximum = -4

d)

minimum = -4
maximum = -6

38.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

39.

If $f\left(x\right)=5^x$ then its inverse is $f^{-1}\left(x\right)=\log_5x$
If f(3) = 125, then what is $f^{-1}\left(125\right)$ ?

a)

-125

b)

-3

c)

3

d)

125

40.

Enter $f\left(x\right)=-\log_2\left(x-2\right)+3$ into your graphing calculator and determine the minimum on interval [ 3, 6 ].

a)

minimum = 3

b)

minimum = 1

c)

minimum = 2

d)

minimum = 6

41.

Determine the inverse of $f\left(x\right)=\log_4x$

a)

$f^{-1}\left(x\right)=x^4$

b)

$f^{-1}\left(x\right)=4^x$

c)

$f^{-1}\left(x\right)=4x$

42.

Determine the inverse of $f\left(x\right)=7^x$

a)

$f^{-1}\left(x\right)=\log_7x$

b)

$f^{-1}\left(x\right)=\log_x7$

c)

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

43.

What is the range of the graph?

a)

$\left(\infty,\ -2\right)$

b)

$\left(-2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)$

44.

Given the parent function $f\left(x\right)=e^x$ , write a function with the transformations: reflection over the x-axis, vertical stretch by a factor of 2, translated right 4 and up 2.

a)

$f\left(x\right)=-2e^{\left(x+4\right)}+2$

b)

$f\left(x\right)=-2e^{\left(x-4\right)}+2$

c)

$f\left(x\right)=-2e^{\left(x-4\right)}-2$

45.

What is the range of this graph?

a)

y = 6

b)

(0, -4)

c)

y > -6

d)

y < -6

46.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

a)

Vertically stretched by a factor of 2, right 3, and up 1

b)

Vertically compressed by a factor of 1/2, left 3 and down 1

c)

Vertically compressed by a factor of 1/2, right 3, and down 1

d)

Vertically stretched by a factor of 2, left 3, and up 1

47.

What equation would yield a transformation right 3 units if your initial function was y=2^x

a)

y=2^x-3

b)

y=2^x+3

c)

y=2^x+³

d)

y=2^x-³

48.

What is the transformation?

a)

Horizontal Translation left 2

b)

Vertical Translation down 2

c)

Reflection over the y-axis

d)

Reflection over the x-axis

49.

$f\left(x\right)=4\left(2\right)^x$ Determine the y-intercept. Enter into the calculator if needed or substitute 0 for x and solve for y.

a)

$\left(0,\ 2\right)$

b)

$\left(0,\ 4\right)$

c)

$\left(0,\ 1\right)$

50.

Find the corresponding graph of
$-\log_4\left(x+1\right)+2$

a)

b)

c)

d)

51.

What is the first step when solving this square root equation $14=4\sqrt{x+3}-6$ ?

a)

Subtract 6 from both sides

b)

Add 6 to both sides

c)

Divide both sides by 4

d)

Square both sides

52.

Describe the transformation.

a)

Down 1

b)

Reflect over y-axis

c)

Up 1

d)

Reflect over x-axis

53.

What are the x-and y-intercepts of $y=\sqrt{x+4}-4$ ? Confirm your answers by graphing and viewing the table.

a)

x-int = (12, 0) and y-int = (0, -2)

b)

x-int = (4, 0) and y-int = (0, 2)

c)

x-int = (0, -4) and y-int = (0, -2)

d)

x-int = (-2, 0) and y-int = (0, 12)

54.

What is the inverse function of $f\left(x\right)\ =\ \left(x\ -\ 2\right)^2$ with a domain of $x\ge2$ ?

a)

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

b)

$f\left(x\right)=\sqrt{x-2}$

c)

$f\left(x\right)\ =\ \sqrt{x}+2$

d)

$f\left(x\right)=\sqrt{x+2}$

55.

What is the minimum of the function $f\left(x\right)=3\sqrt{x-2}+4$ (shown in the graph) on the interval [3,9]?

a)

3

b)

5

c)

7

d)

4

56.

Enter $f\left(x\right)=-\sqrt{x-5}+1$ into your calculator. Determine the min and max values on the interval [6, 21] by looking at the table.

a)

$\min=-3;\ \max=0$

b)

$\min=0;\ \max=-3$

c)

$\min=-4;\ \max\ =\ 1$

57.

What are the transformations for the graph of

the parent function f(x) = √x to the function above

a)

Vertical Stretch by a factor of 2; translated down 5 units

b)

Horizontal Shrink by 1/2, and down 5 units

c)

Vertical Shrink by a factor of 2; translated left 5 units

d)

Vertical trSetch by a factor of 2; translated right one unit

58.

Which of the following is the domain shown in the graph?

a)

[4,∞)

b)

[-4,∞)

c)

(4,8)

d)

[-4,8]

59.

What is the inverse of the function $y=x^2$

a)

$y=2^x$

b)

$y=\log_2x$

c)

$y=2x$

d)

$y=\sqrt{x}$

60.

Are the graphs inverses?

a)

yes

b)

no

61.

Find the inverse function of $f\left(x\right)=\sqrt{x}-6$

a)

$y=\left(x+6\right)^2$ w/ domain $x\ge-6$

b)

$y=\left(x-6\right)^2$ w/ domain $x\ge6$

c)

$y=x^2+6$ w/ domain $x\ge0$

d)

$y=x^2+36$ w/ domain $x\ge0$

62.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

63.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

64.

What is the least common multiple of x²-16 and x²+4x-32?

a)

(x + 4)(x – 4)(x + 8)

b)

(x-4)2 (x+8)

c)

(x + 4)(x – 4)

d)

(x - 4)(x-4)2(x + 8)

65.

Describe the transformation from the parent function.

a)

left 4

b)

up 4

c)

right 5, up 4

d)

left 5, up 4

66.

Describe the transformation:

a)

Right 1, down 3

b)

Down 3

c)

Left 1, Down 3

d)

Up 1, left 1, down 3

67.

Describe all transformations from the parent function g(x)=1/x to f(x).

a)

Shift right 5 and shift up 7

b)

Shift left 7 and shift up 5

c)

Reflect over the x-axis, shift up 7

d)

Shift left 5 and shift up 7

68.

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

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

69.

Logarithms and Exponentials are what?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

70.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

71.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

72.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

73.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

74.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

75.

Add

a)

A.

b)

B.

c)

C.

d)

D.

76.

a)

b)

c)

d)

Final Exam Review 2023

Total questions: 76

Worksheet time: 4hrs 19mins

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