Exponential and Logarithmic Functions: Interactive Quizzes and Practice

Question 1

Which of the following is the graph of the function y = 2^x?

Accepted Answer

An exponential curve that increases rapidly

Answer

A straight line with a positive slope

Answer

A parabola opening upwards

Answer

A logarithmic curve that decreases rapidly

Question 2

Which of the following is the inverse function of y = log2(x)?

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = 2log(x)

Answer

y = log2(x^2)

Question 3

Find the equation of the exponential function that passes through the points (1, 2) and (3, 8).

Accepted Answer

y = 2^(x+1)

Answer

y = 2^(x-1)

Answer

y = 2x

Answer

y = 4^x

Question 4

Find the value of x that satisfies the equation: 2^x * 4^x = 16^x

Accepted Answer

1

Answer

0

Answer

2

Answer

4

Question 5

Find the derivative of the function y = e^x

Accepted Answer

y' = e^x

Answer

y' = x*e^x

Answer

y' = 1/e^x

Answer

y' = 0

Question 6

Define the natural logarithm and explain how it relates to the common logarithm.

Accepted Answer

The natural logarithm is the inverse of the exponential function with base e. The common logarithm is the inverse of the exponential function with base 10.

Answer

The natural logarithm and the common logarithm are equal.

Answer

The natural logarithm is always positive.

Answer

The common logarithm is only defined for values of x greater than 1.

Question 7

Which of the following is the graph of the exponential function f(x) = 2^x?

Accepted Answer

A curve that increases rapidly as x increases, with no upper or lower bounds.

Answer

A parabola opening upwards.

Answer

A parabola opening downwards.

Answer

A straight line with a positive slope.

Question 8

Determine the domain of the function f(x) = log_2(x - 3).

Accepted Answer

(3, ∞)

Answer

[0, ∞)

Answer

(-∞, 3)

Answer

All real numbers

Question 9

Identify the inverse of the function f(x) = 3^x.

Accepted Answer

f^-1(x) = log_3(x)

Answer

f^-1(x) = x^3

Answer

f^-1(x) = e^x

Answer

f^-1(x) = ln x

Question 10

Determine the equation of the line of symmetry of the function f(x) = 2^x + 3.

Accepted Answer

y = 3

Answer

y = -3

Answer

x = 3

Answer

x = -3

Question 11

Which of the following graphs represents the function f(x) = 2^x? (Exponential Function)

Accepted Answer

An upward-curving line passing through the point (0, 1) and continuously increasing.

Answer

A downward-curving line passing through the point (0, 1) and continuously decreasing.

Answer

A straight line passing through the point (0, 1).

Question 12

What is the domain of the function f(x) = log(x - 2)? (Logarithmic Function)

Accepted Answer

x > 2

Answer

x < 2

Answer

All real numbers.

Answer

x ≥ 2

Question 13

The half-life of a radioactive substance is 100 years. If there are initially 1000 grams of the substance present, how many grams will be present after 200 years? (Exponential Function Application)

Accepted Answer

250 grams

Answer

750 grams

Answer

500 grams

Question 14

Which of the following equations represents an exponential growth model? (Exponential Growth Model)

Accepted Answer

y = Ce^(kt)

Answer

y = C - kt

Answer

y = C + kt

Question 15

Which of the following functions is a logarithmic transformation? (Logarithmic Transformation)

Accepted Answer

f(x) = log(x + 1)

Answer

f(x) = sin(x)

Answer

f(x) = x^2 + 1

Answer

f(x) = e^x

Question 16

Find the derivative of the function f(x) = 2^x. (Derivative of Exponential Function)

Accepted Answer

f'(x) = 2^x * log(2)

Answer

f'(x) = 2^x

Answer

f'(x) = log(2^x)

Answer

f'(x) = x * 2^(x-1)

Question 17

Which of the following best describes the graph of the exponential function y = 2^x?

Accepted Answer

A curve that rises steeply as x increases

Answer

A straight line with a positive slope

Answer

A curve that levels off as x increases

Answer

A parabola that opens upwards

Question 18

Evaluate log₂ 16.

Accepted Answer

4

Answer

16

Answer

8

Answer

2

Question 19

Find the inverse function of y = log₂ x.

Accepted Answer

y = 2^x

Answer

y = e^x

Answer

y = x^2

Answer

y = log₁₀ x

Question 20

Determine the domain of the function y = ln(x).

Accepted Answer

x > 0

Answer

x ≥ 0

Answer

x < 0

Answer

All real numbers

Question 21

Which logarithmic property is used in the equation: log(a * b) = log(a) + log(b)?

Accepted Answer

Product Rule of Logarithms

Answer

Change of Base Formula

Answer

Power Rule of Logarithms

Answer

Quotient Rule of Logarithms

Question 22

Find the inverse function of y = 3^x

Accepted Answer

y = log3(x)

Answer

y = 3^(-x)

Answer

y = x^3

Answer

y = 1/3^x

Question 23

Solve for x: log2(x) + log2(x-3) = 2

Accepted Answer

x = 8

Answer

x = 12

Answer

x = 6

Answer

x = 4

Question 24

Determine the equation of the exponential function that passes through the points (1, 2) and (2, 4)

Accepted Answer

y = 2^x

Answer

y = e^x

Answer

y = 3^x

Answer

y = 10^x

Question 25

Which of the following represents the graph of the exponential function, f(x) = 2^x?

Accepted Answer

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

Answer

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

Answer

A straight line with a positive gradient

Question 26

Identify the equation of the logarithmic function whose graph passes through the point (1, 2).

Accepted Answer

y = log2(x)

Answer

y = x^2

Answer

y = 2x

Question 27

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

Accepted Answer

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

Answer

f^-1(x) = e^x

Answer

f^-1(x) = 2^-x

Answer

f^-1(x) = x^2

Question 28

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

Accepted Answer

x > 1

Answer

All real numbers

Answer

x < 1

Answer

x > 0

Question 29

Identify the range of the function f(x) = 2^x.

Accepted Answer

y > 0

Answer

y < 0

Answer

y > 1

Answer

All real numbers

Question 30

What is the equation of the asymptote for the graph of the function f(x) = log2(x)?

Accepted Answer

y = 0

Answer

y = 1

Answer

x = 1

Answer

x = 0

Question 31

Find the derivative of the function f(x) = 2^x.

Accepted Answer

f'(x) = 2^x * ln(2)

Answer

f'(x) = 2^x

Answer

f'(x) = ln(2^x)