Exponential and Logarithmic Functions: Interactive Quizzes and Practice

Question 1

Which of the following is the domain of the function y = e^(x-2)?

Accepted Answer

All real numbers

Answer

x < 2

Answer

x > 2

Answer

x ≠ 2

Question 2

Solve the exponential inequality: 2^x > 8

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 2

Answer

x < 2

Question 3

What is the equation of the horizontal asymptote of the logarithmic function f(x) = (1/2)^x + 1?

Accepted Answer

y = 1

Answer

y = 0

Answer

x = 0

Answer

x = 1

Question 4

Which graph represents the function f(x) = 2^x + 1?

Accepted Answer

An exponential curve showing rapid growth

Answer

A straight line with a positive slope

Answer

A parabola with its opening facing up

Answer

A logarithmic curve showing rapid decay

Question 5

Which graph best represents the function f(x) = 2^x - 3?

Accepted Answer

B: An upward-opening exponential curve shifted down 3 units

Answer

A: An upward-opening parabola shifted down 3 units

Answer

C: A downward-opening exponential curve shifted down 3 units

Answer

D: A straight line shifted down 3 units

Question 6

Find the domain of the function f(x) = ln(x-2)

Accepted Answer

x > 2

Answer

x < 2

Answer

x > 0

Answer

All real numbers

Question 7

What is the equation of the horizontal asymptote of the function f(x) = e^(-x)?

Accepted Answer

y = 0

Answer

y = 1

Answer

y = e

Answer

y = -1

Question 8

What is the equation of a logarithmic function with base 10?

Accepted Answer

y = log10(x)

Answer

y = 10x

Answer

y = x^10

Answer

y = 1/x

Question 9

What is the domain of the function f(x) = log2(x - 1)?

Accepted Answer

x > 1

Answer

x < 1

Answer

x ≥ 1

Answer

x ≤ 1

Question 10

What is the growth factor of the exponential function f(x) = 3^x?

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 11

What is the inverse function of f(x) = log2(x)?

Accepted Answer

f^-1(x) = 2^x

Answer

f^-1(x) = log2(x)

Answer

f^-1(x) = x^2

Answer

f^-1(x) = 1/log2(x)

Question 12

Solve for x: 2^x - 3 = 5

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 3

Answer

x = 5

Question 13

What is the domain of the function y = ln(x^2 - 4)?

Accepted Answer

x < -2 or x > 2

Answer

x > 2

Answer

x > 0

Answer

All real numbers

Question 14

Which function is the inverse of y = 2^x?

Accepted Answer

y = log2(x)

Answer

y = 1/2^x

Answer

y = x^2

Answer

y = e^x

Question 15

Identify the graph that accurately represents the exponential function f(x) = 2^x.

Accepted Answer

An upward-sloping curve passing through the point (0, 1)

Answer

A horizontal line passing through the point (0, 2)

Answer

A downward-sloping curve passing through the point (1, 0)

Question 16

Which function among the following is monotonically increasing?

Accepted Answer

f(x) = 3^(x - 2)

Answer

h(x) = log(x + 2)

Answer

g(x) = 10^(-x)

Answer

j(x) = ln(x - 1)

Question 17

Determine the equation of the horizontal asymptote for the graph of the function f(x) = 1 + e^(-x).

Accepted Answer

y = 1

Answer

y = 0

Answer

y = -1

Answer

y = 2

Question 18

Provide a real-world application of exponential functions.

Accepted Answer

Modeling radioactive decay

Answer

Solving quadratic equations

Answer

Measuring the height of a tree

Answer

Calculating the area of a circle

Question 19

Express the exponential equation 5^2 = 25 in logarithmic form.

Accepted Answer

log(25, 5) = 2

Answer

log(2, 25) = 5

Answer

log(5, 25) = 2

Answer

log(25, 2) = 5

Question 20

Which of the following is the equation of the exponential graph shown below?

[Image of an exponential graph with base 2]

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = log_2(x)

Answer

y = e^x

Question 21

Which of the following equations represents an exponential decay function?

Accepted Answer

y = 2^(-x)

Answer

y = x^3

Answer

y = ln(x)

Question 22

Which of the following is the graph of the logarithmic function f(x) = log_3(x)?

[Image of a logarithmic graph with base 3]

Accepted Answer

[Image of a logarithmic graph with base 3]

Answer

[Image of a linear graph]

Answer

[Image of a logarithmic graph with base 10]

Answer

[Image of an exponential graph with base 3]

Question 23

Simplify the expression log_4(16) + log_4(2).

Accepted Answer

3

Answer

2

Answer

6

Answer

4

Question 24

Find the equation of the vertical asymptote of the function f(x) = ln(x - 2).

Accepted Answer

x = 2

Answer

y = 0

Answer

y = 2

Answer

x = 0

Question 25

Which of the following is an example of an exponential function used in the real world?

Accepted Answer

Radioactive decay

Answer

Calculating the area of a triangle

Answer

Finding the volume of a cone

Answer

Solving linear equations

Question 26

The population of a city is growing exponentially. If the population was 100,000 in 2010 and 150,000 in 2020, what is the approximate annual growth rate?

Accepted Answer

4.14%

Answer

2.75%

Answer

3.50%

Answer

5.00%

Question 27

Which of the following functions represents exponential decay?

Accepted Answer

f(x) = 2^(-x)

Answer

f(x) = 1/x

Answer

f(x) = x^2

Answer

f(x) = 3^x

Question 28

The graph of the function y = log₂(x) passes through which of the following points?

Accepted Answer

(4, 2)

Answer

(2, 4)

Answer

(1, 0)

Question 29

What is the value of log₃(81)?

Accepted Answer

4

Answer

27

Answer

3

Answer

9

Question 30

Which of the following is equivalent to the expression ln(e^5)?

Accepted Answer

5

Answer

e^5

Answer

ln(5)

Answer

1/5

Question 31

Solve for x: 2^(x+1) = 16

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 1

Answer

x = 4

Question 32

The half-life of a radioactive substance is 10 years. If you start with 100 grams of the substance, how many grams will remain after 30 years?

Accepted Answer

12.5 grams

Answer

75 grams

Answer

50 grams

Answer

25 grams

Question 33

The pH of a solution is defined as pH = -log[H+], where [H+] is the concentration of hydrogen ions. If the pH of a solution is 4, what is the concentration of hydrogen ions?

Accepted Answer

10^(-4) moles/liter

Answer

10^4 moles/liter

Answer

4 moles/liter

Answer

0.04 moles/liter

Question 34

Which of the following is the inverse function of f(x) = e^(2x)?

Accepted Answer

g(x) = ln(x)/2

Answer

g(x) = 2ln(x)

Answer

g(x) = e^(-2x)

Answer

g(x) = ln(2x)

Question 35

The intensity of sound is measured in decibels (dB). The formula for decibel level is L = 10log(I/I₀), where I is the intensity of the sound and I₀ is the threshold of hearing. If the intensity of a sound is 100 times the threshold of hearing, what is the decibel level?

Accepted Answer

20 dB

Answer

100 dB

Answer

10 dB

Answer

50 dB