Free Printable Unit 5 Review (Exponential and Logarithmic Functions)

1.

Which equation is the general form of an exponential equation?

a)

$y=ab^x$

b)

$y=mx+b$

c)

$a^2+b^2=c^2$

d)

$y=\log\left(x\right)$

2.

Which equation is the general form of a logarithmic equation?

a)

$y=ab^x$

b)

$y=mx+b$

c)

$a^2+b^2=c^2$

d)

$y=\log\left(x\right)$

3.

Determine the transformation that occurred:

\log\left(x\right)\ \rightarrow\ \log\left(x-4\right)

a)

Horizontal shift, 4 units left

b)

Horizontal shift, 4 units right

c)

Vertical shift, 4 units up

d)

Vertical shift, 4 units down

4.

Determine the transformation that occurred:

\log\left(x\right)\ \rightarrow\ \log\left(x+4\right)

a)

Horizontal shift, 4 units left

b)

Horizontal shift, 4 units right

c)

Vertical shift, 4 units up

d)

Vertical shift, 4 units down

5.

Determine the transformation that occurred:

\log\left(x\right)\ \rightarrow\ \log\left(x\right)+4

a)

Horizontal shift, 4 units left

b)

Horizontal shift, 4 units right

c)

Vertical shift, 4 units up

d)

Vertical shift, 4 units down

6.

Determine the transformation that occurred:

\log\left(x\right)\ \rightarrow\ \log\left(x\right)-4

a)

Horizontal shift, 4 units left

b)

Horizontal shift, 4 units right

c)

Vertical shift, 4 units up

d)

Vertical shift, 4 units down

7.

When two functions are inverses of each other, what is known about their coordinate points?

a)

The coordinate points are switched from (x, y) to (y, x)

b)

Their coordinate points do not change.

c)

Their coordinate points change by a scale factor of 2.

d)

Their coordinate points change by a scale factor of 1/2.

8.

When two functions are inverses of each other, which line did they reflect over?

a)

y = x

b)

y = -x

c)

x-axis

d)

y-axis

9.

Identify the growth factor in the given function:

B\left(t\right)=750\left(1.16\right)^t

a)

750

b)

1.16

c)

0.16

d)

t

10.

Identify the rate in the given function:

B\left(t\right)=750\left(1.16\right)^t

a)

750

b)

1.16

c)

0.16

d)

t

11.

Identify the variable that represents "time" in the given function:

B\left(t\right)=750\left(1.16\right)^t

a)

750

b)

B(t)

c)

0.16

d)

t

12.

Identify the initial value in the given function:

B\left(t\right)=750\left(1.16\right)^t

a)

750

b)

1.16

c)

0.16

d)

t

13.

Which sketch best represents the graph of

x=3^y

?

a)

b)

c)

d)

14.

Which statement about the graph of

c\left(x\right)=\log_6\left(x\right)

is false?

a)

The asymptote has equation y = 0.

b)

The graph has no y-intercept.

c)

The domain is the set of positive reals.

d)

The range is the set of all real numbers.

15.

The graph of

y=\log_2\left(x\right)\

is translated to the right 1 unit and down 1 unit. The coordinates of the x-intercept of the translated graph are

a)

(0, 0)

b)

(1, 0)

c)

(2, 0)

d)

(3, 0)

16.

If

f\left(x\right)=\log_3\left(x\right)

and

g\left(x\right)

is the image of

f\left(x\right)

after a translation five units to the left, which equation represents

g\left(x\right)

?

a)

$g\left(x\right)=\log_3\left(x+5\right)$

b)

$g\left(x\right)=\log_3\left(x\right)+5$

c)

$g\left(x\right)=\log_3\left(x-5\right)$

d)

$g\left(x\right)=\log_3\left(x\right)-5$

17.

If $ae^{bt}=c$ , where a, b, and c are positive, then t equals

a)

$\ln\left(\frac{c}{ab}\right)$

b)

$\ln\left(\frac{cb}{a}\right)$

c)

$\frac{\ln\left(\frac{c}{a}\right)}{b}$

d)

$\frac{\ln\left(\frac{c}{a}\right)}{\ln\left(b\right)}$

18.

The value of $\log\left(1\right)=$

a)

0

b)

1

c)

10

d)

There is no value

19.

If there is no visible base in the function $y=\log\left(x\right)$ , then the default base is

a)

10

b)

1

c)

0

d)

e

20.

The logarithm $y=\log_e\left(x\right)$ is the same as $y=\ln\left(x\right)$

a)

True

b)

False

21.

Identify which formula is the "product rule of logarithms".

a)

$\log\left(mn\right)=\log\left(m\right)+\log\left(n\right)$

b)

$\log\left(\frac{m}{n}\right)=\log\left(m\right)-\log\left(n\right)$

c)

$\log\left(m^a\right)=a\log\left(m\right)$

d)

$\log_a\left(x\right)=\frac{\log\left(x\right)}{\log\left(a\right)}$

22.

Identify which formula is the "quotient rule of logarithms".

a)

$\log\left(mn\right)=\log\left(m\right)+\log\left(n\right)$

b)

$\log\left(\frac{m}{n}\right)=\log\left(m\right)-\log\left(n\right)$

c)

$\log\left(m^a\right)=a\log\left(m\right)$

d)

$\log_a\left(x\right)=\frac{\log\left(x\right)}{\log\left(a\right)}$

23.

Identify which formula is the "power rule of logarithms".

a)

$\log\left(mn\right)=\log\left(m\right)+\log\left(n\right)$

b)

$\log\left(\frac{m}{n}\right)=\log\left(m\right)-\log\left(n\right)$

c)

$\log\left(m^a\right)=a\log\left(m\right)$

d)

$\log_a\left(x\right)=\frac{\log\left(x\right)}{\log\left(a\right)}$

24.

Identify which formula is the "change of base" for logarithms.

a)

$\log\left(mn\right)=\log\left(m\right)+\log\left(n\right)$

b)

$\log\left(\frac{m}{n}\right)=\log\left(m\right)-\log\left(n\right)$

c)

$\log\left(m^a\right)=a\log\left(m\right)$

d)

$\log_a\left(x\right)=\frac{\log\left(x\right)}{\log\left(a\right)}$

25.

Which choice expresses $\log_5\left(8\right)$ as a change of base?

a)

$\frac{\ln\left(8\right)}{\ln\left(5\right)}$

b)

$\frac{\ln\left(5\right)}{\ln\left(8\right)}$

c)

$\log_8\left(5\right)$

d)

$\frac{\log_3\left(8\right)}{\log_7\left(5\right)}$

26.

Express the given logarithm as an exponential equation:

\log_{15}\left(225\right)=2

a)

$15^2=225$

b)

$225^2=15$

c)

$2^{15}=225$

d)

$255^{15}=2$

27.

Express the given logarithm as an exponential equation:

\log_3\left(\frac{1}{27}\right)=-3

a)

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

b)

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

c)

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

d)

$\left(\frac{1}{27}\right)^{-3}=3$

28.

Which general equation represents the "natural logarithm"?

a)

$y=\ln\left(x\right)$

b)

$y=mx+b$

c)

$y=ax^2+bx+c$

d)

$y=ab^x$

29.

Which general equation represents the "quadratic equation"?

a)

$y=\ln\left(x\right)$

b)

$y=mx+b$

c)

$y=ax^2+bx+c$

d)

$y=ab^x$

30.

Which general equation represents the "linear equation"?

a)

$y=\ln\left(x\right)$

b)

$y=mx+b$

c)

$y=ax^2+bx+c$

d)

$y=ab^x$

31.

Which general equation represents the "exponential equation"?

a)

$y=\ln\left(x\right)$

b)

$y=mx+b$

c)

$y=ax^2+bx+c$

d)

$y=ab^x$

32.

The inverse of the exponential equation,

y=2^x

, is

a)

$y=\log_2\left(x\right)$

b)

$y=\log_x\left(2\right)$

c)

$2=\log_y\left(x\right)$

d)

$x=\log_2\left(y\right)$

33.

Solve the given equation for x:

\log_4\left(x\right)+\log_4\left(x-6\right)=2

a)

x = 8, x = -2

b)

x = -8, x = -2

c)

x = -8, x = 2

d)

x = 8, x = 2

34.

Which expression is not equivalent to

8+\left(n-4\right)

a)

$12+n$

b)

$n+4$

c)

$\left(8+n\right)-4$

d)

$\left(8-4\right)+n$

35.

When you read the word "difference", which operation should you use?

a)

addition

b)

subtraction

c)

multiplication

d)

division

36.

When you read the word "sum", which operation should you use?

a)

addition

b)

subtraction

c)

multiplication

d)

division

37.

When you read the word "quotient", which operation should you use?

a)

addition

b)

subtraction

c)

multiplication

d)

division

38.

When you read the word "product", which operation should you use?

a)

addition

b)

subtraction

c)

multiplication

d)

division

39.

Which symbol represents "less than"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

40.

Which symbol represents "less than or equal to"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

41.

Which symbol represents "greater than or equal to"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

42.

Which symbol represents "greater than"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

43.

Which formula is used for compound interest?

a)

$y=ab^x$

b)

$y=a\left(1+r\right)^t$

c)

$y=a\left(1+\frac{r}{n}\right)^{nt}$

d)

$y=Pe^{rt}$

44.

Which formula is used for continuous compound interest?

a)

$y=ab^x$

b)

$y=a\left(1+r\right)^t$

c)

$y=a\left(1+\frac{r}{n}\right)^{nt}$

d)

$y=Pe^{rt}$

45.

Growth factor and growth rate are the same thing.

a)

True

b)

False

46.

When an account is compounded weekly, the interest rate compounds how many times a year?

a)

1

b)

2

c)

12

d)

52

47.

When an account is compounded daily, the interest rate compounds how many times a year?

a)

365

b)

2

c)

12

d)

52

48.

When an account is compounded monthly, the interest rate compounds how many times a year?

a)

1

b)

2

c)

12

d)

52

49.

When an account is compounded semi-annually, the interest rate compounds how many times a year?

a)

1

b)

2

c)

12

d)

52

50.

When an account is compounded annually, the interest rate compounds how many times a year?

a)

1

b)

2

c)

12

d)

52

51.

When a bank account compounds continuously, the base of the exponential function representing this situation is

a)

e

b)

2

c)

$\pi$

d)

There is no base

52.

When two linear equations intersect and form a 90 degree angle, they are known as...

a)

parallel lines

b)

perpendicular lines

c)

lines that do not intersect

d)

lines that overlap

53.

When two linear equations have the same slope, they are known as...

a)

parallel lines

b)

perpendicular lines

c)

lines that do not intersect

d)

lines that overlap

54.

The following is an example of a complex number:

36+5i

a)

True

b)

False

55.

A complex number consists of both real and imaginary parts but either part can be 0.

a)

True

b)

False

56.

The absolute value is the distance between a number and zero.

a)

True

b)

False

57.

The zero exponent rule states that any number or variable raised to the 0 power is 0.

a)

True

b)

False

58.

Which expression represents the power rule of exponents?

a)

$a^m\cdot a^n=a^{\left(m+n\right)}$

b)

$\frac{a^m}{a^n}=a^{\left(m-n\right)}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

$a^{-m}=\frac{1}{a^m}$

59.

Which expression represents the product rule of exponents?

a)

$a^m\cdot a^n=a^{\left(m+n\right)}$

b)

$\frac{a^m}{a^n}=a^{\left(m-n\right)}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

$a^{-m}=\frac{1}{a^m}$

60.

Which expression represents the quotient rule of exponents?

a)

$a^m\cdot a^n=a^{\left(m+n\right)}$

b)

$\frac{a^m}{a^n}=a^{\left(m-n\right)}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

$a^{-m}=\frac{1}{a^m}$

61.

Which expression represents the negative exponent rule of exponents?

a)

$a^m\cdot a^n=a^{\left(m+n\right)}$

b)

$\frac{a^m}{a^n}=a^{\left(m-n\right)}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

$a^{-m}=\frac{1}{a^m}$

62.

Which expression represents the quotient of

\left(y^2-4y-32\right)\div\left(y+4\right)

a)

$y-8$

b)

$y-4$

c)

$y+8$

d)

$y+4$

63.

Select all expressions that are classified as monomials.

a)

$9x$

b)

$3t^2+5t+8$

c)

$11xy^5$

d)

$\frac{1}{2}m+6p$

64.

The zero exponent rule states that any number or variable raised to the 0 power is 1.

a)

True

b)

False

65.

A trinomial is an expression that contains __ terms.

a)

1

b)

2

c)

3

d)

4

66.

A binomial is an expression that contains __ terms.

a)

1

b)

2

c)

3

d)

4

67.

A monomial is an expression that contains __ terms.

a)

1

b)

2

c)

3

d)

4

68.

Determine the transformation that occurred:

y=e^x\ \rightarrow\ y=e^{\left(x+4\right)}-1

a)

Horizontal shift left 4, Vertical shift down 1

b)

Horizontal shift right 4, Vertical shift down 1

c)

Horizontal shift left 4, Vertical shift up 1

d)

Horizontal shift right 4, Vertical shift up 1

69.

Determine the transformation that occurred:

y=e^x\ \rightarrow\ y=e^{\left(x-4\right)}-1

a)

Horizontal shift left 4, Vertical shift down 1

b)

Horizontal shift right 4, Vertical shift down 1

c)

Horizontal shift left 4, Vertical shift up 1

d)

Horizontal shift right 4, Vertical shift up 1

70.

Determine the transformation that occurred:

y=e^x\ \rightarrow\ y=e^{\left(x+4\right)}+1

a)

Horizontal shift left 4, Vertical shift down 1

b)

Horizontal shift right 4, Vertical shift down 1

c)

Horizontal shift left 4, Vertical shift up 1

d)

Horizontal shift right 4, Vertical shift up 1

71.

Determine the transformation that occurred:

y=e^x\ \rightarrow\ y=e^{\left(x-4\right)}+1

a)

Horizontal shift left 4, Vertical shift down 1

b)

Horizontal shift right 4, Vertical shift down 1

c)

Horizontal shift left 4, Vertical shift up 1

d)

Horizontal shift right 4, Vertical shift up 1

72.

Determine the degree of the given expression:

12x^5+5x^3-7x

a)

5

b)

12

c)

3

d)

7

73.

The domain of a function are...

a)

All the x-values that satisfy the function.

b)

All the positive x-values that satisfy the function.

c)

All the y-values that satisfy the function.

d)

All the positive y-values that satisfy the function.

74.

The range of a function are...

a)

All the x-values that satisfy the function.

b)

All the positive x-values that satisfy the function.

c)

All the y-values that satisfy the function.

d)

All the positive y-values that satisfy the function.

75.

Given the function, f(x), which expression represents a vertical shift 2 units up?

a)

f(x) + 2

b)

f(x + 2)

c)

f(x) - 2

d)

f(x - 2)

76.

Given the function, f(x), which expression represents a vertical shift 2 units down?

a)

f(x) + 2

b)

f(x + 2)

c)

f(x) - 2

d)

f(x - 2)

77.

Given the function, f(x), which expression represents a horizontal shift 2 units left?

a)

f(x) + 2

b)

f(x + 2)

c)

f(x) - 2

d)

f(x - 2)

78.

Given the function, f(x), which expression represents a horizontal shift 2 units right?

a)

f(x) + 2

b)

f(x + 2)

c)

f(x) - 2

d)

f(x - 2)

79.

Given the function, f(x), which expression represents a reflection over the x-axis AND a horizontal shift 2 units right?

a)

-f(x) + 2

b)

-f(x + 2)

c)

-f(x) - 2

d)

-f(x - 2)

80.

Given the function, f(x), which expression represents a reflection over the x-axis AND a horizontal shift 2 units left?

a)

-f(x) + 2

b)

-f(x + 2)

c)

-f(x) - 2

d)

-f(x - 2)

81.

Given the function, f(x), which expression represents a reflection over the x-axis AND a vertical shift 2 units up?

a)

-f(x) + 2

b)

-f(x + 2)

c)

-f(x) - 2

d)

-f(x - 2)

82.

Given the function, f(x), which expression represents a reflection over the x-axis AND a vertical shift 2 units down?

a)

-f(x) + 2

b)

-f(x + 2)

c)

-f(x) - 2

d)

-f(x - 2)

83.

The graph shown is an example of...?

a)

exponential growth

b)

exponential decay

c)

quadratic growth

d)

linear decay

84.

Simplify the expression:

\sqrt{-25}

a)

5i

b)

5

c)

-5

d)

-5i

85.

Simplify the expression:

-\sqrt{-25}

a)

5i

b)

5

c)

-5

d)

-5i

86.

Simplify the expression:

-\sqrt{25}

a)

5i

b)

5

c)

-5

d)

-5i

87.

Simplify the expression:

\sqrt{25}

a)

5i

b)

5

c)

-5

d)

-5i

88.

Which expression is equivalent to

\left(4i\right)^3

?

a)

-12i

b)

-64i

c)

12i

d)

64i

89.

A circuit has a current of (8+7i) amps, and another circuit has a current of (5−3i) amps. What is the difference between the currents of the two circuits?

a)

(3 - 4i) amps

b)

(3 + 4i) amps

c)

(3 + 10i) amps

d)

(3 - 10i) amps

90.

Evaluate the expression

\log_4\left(16\right)

a)

2

b)

0.5

c)

1.204

d)

0.602

91.

Evaluate the expression

\left(45e^6\right)^0

a)

1

b)

0

c)

403.429

d)

122.323

92.

Simplify the given expression:

i^4

a)

i

b)

-1

c)

-i

d)

1

93.

Simplify the given expression:

i^3

a)

i

b)

-1

c)

-i

d)

1

94.

Simplify the given expression:

i^2

a)

i

b)

-1

c)

-i

d)

1

95.

Identify the base of the given logarithmic equation:

y=\log_5\left(x+1\right)-2

a)

5

b)

-1

c)

1

d)

-2

96.

Which formula is used to find the slope of a line when given two coordinate points?

a)

$m=\frac{y_2-y_1}{x_2-x_1}$

b)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

c)

$a^2+b^2=c^2$

d)

$y=mx+b$

97.

Which formula is used to find the missing side of a right triangle when given the side lengths of a hypotenuse and leg?

a)

$m=\frac{y_2-y_1}{x_2-x_1}$

b)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

c)

$a^2+b^2=c^2$

d)

$y=mx+b$

98.

Which formula is used to find the roots or zeros of a quadratic equation?

a)

$m=\frac{y_2-y_1}{x_2-x_1}$

b)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

c)

$a^2+b^2=c^2$

d)

$y=mx+b$

99.

Based on the given equation, identify its horizontal asymptote: $y=15\left(2\right)^x+9$

a)

y = 9

b)

y = 2

c)

y = 15

d)

x = 9

100.

Based on the given equation, identify its initial value: $y=15\left(2\right)^x+9$

a)

9

b)

2

c)

15

d)

9

Unit 5 Review (Exponential and Logarithmic Functions)

Total questions: 100

Worksheet time: 2hrs 42mins

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