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AP PreCalculus Practice Quiz: Exponential Functions

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 12 questions to check your progress.

Question 1 of 12

In the exponential function f(x) = 7(1.5)^{x}, what does the value 7 represent?

All Questions (12)

In the exponential function f(x) = 7(1.5)^{x}, what does the value 7 represent?

A) The base

B) The initial value

C) The exponent

D) The domain

Correct Answer: B

Based on the general form f(x) = ab^{x}, the coefficient 'a' represents the initial value of the function. In this case, a = 7.

What is the domain of any function in the general form f(x) = ab^{x}?

A) All positive real numbers

B) All real numbers except 0

C) All integers

D) All real numbers

Correct Answer: D

The provided content explicitly states that the domain of an exponential function is all real numbers.

Which of the following functions does NOT satisfy the definition of an exponential function in the general form f(x) = ab^{x}?

A) f(x) = 5(1)^{x}

B) f(x) = -2(3)^{x}

C) f(x) = 0.5(0.2)^{x}

D) f(x) = 10(4)^{x}

Correct Answer: A

According to the definition, the base 'b' of an exponential function must be greater than 0 and not equal to 1 (b > 0, b ≠ 1). In option A, the base is 1, which results in a constant function, not an exponential one.

Consider the function f(x) = 3(0.4)^{x}. Which statement best describes the end behavior of the function as the input values increase without bound?

A) The output values increase without bound.

B) The output values decrease without bound.

C) The output values get arbitrarily close to zero.

D) The output values get arbitrarily close to 3.

Correct Answer: C

For an exponential function with a base 'b' between 0 and 1 (0 < b < 1), the function represents exponential decay. As the input 'x' increases, the output values will get arbitrarily close to zero.

A function's graph is known to be always increasing and always concave up. Based on the key characteristics of exponential functions, which of the following could be its equation?

A) f(x) = 2(0.8)^{x}

B) f(x) = 2(5)^{x}

C) f(x) = -2(5)^{x}

D) f(x) = x^{2}

Correct Answer: B

Exponential functions are always concave up when the initial value 'a' is positive. They are always increasing when the base 'b' is greater than 1. Option B, f(x) = 2(5)^{x}, satisfies both conditions (a=2 > 0 and b=5 > 1).

Let g(x) = f(x) + 10 be an additive transformation of a function f(x). If it is determined that the values of g(x) are proportional over equal-length input-value intervals, what must be true about f(x)?

A) f(x) is linear.

B) f(x) is quadratic.

C) f(x) is exponential.

D) f(x) is constant.

Correct Answer: C

The provided content states: 'If the values of the additive transformation function g(x) = f(x) + k of any function f are proportional over equal-length input-value intervals, then f is exponential.' This question is a direct application of that rule.

Which of the following is a key characteristic of all exponential functions in the form f(x) = ab^{x}?

A) The graph has a vertex.

B) The graph is always increasing or always decreasing.

C) The range is all real numbers.

D) The graph is a straight line.

Correct Answer: B

The content specifies that 'Exponential functions are always increasing or always decreasing'. They do not change direction like a parabola (which has a vertex) or have a range of all real numbers.

In the general form f(x) = ab^{x}, the condition a ≠ 0 is required because if a = 0, the function would be:

A) f(x) = b^{x}, a simpler exponential function

B) f(x) = 0, a constant function

C) undefined for most values of x

D) a linear function with a slope of b

Correct Answer: B

If a=0, the function becomes f(x) = 0 * b^{x} = 0 for all values of x. This is the constant function f(x) = 0, not an exponential function.

Consider the function g(x) = f(x) - 5. The table below shows values for g(x). Based on this data, is f(x) an exponential function? | x | g(x) | |---|---| | 1 | 1 | | 2 | 7 | | 3 | 25 | | 4 | 79 |

A) Yes, because the differences between consecutive g(x) values have a common ratio.

B) No, because the g(x) values do not have a common ratio.

C) Yes, because the g(x) values have a common difference.

D) No, because the differences between consecutive g(x) values are not proportional.

Correct Answer: A

To test if f(x) is exponential, we check if the differences in g(x) values are proportional (have a common ratio). The differences are: 7-1=6, 25-7=18, 79-25=54. The ratios of these differences are 18/6 = 3 and 54/18 = 3. Since the differences have a common ratio of 3, f(x) is an exponential function.

For the exponential function f(x) = 100(2)^{x}, what happens to the output values as the input values increase without bound?

A) They get arbitrarily close to 100.

B) They get arbitrarily close to 0.

C) They increase without bound.

D) They decrease without bound.

Correct Answer: C

The function has a base b=2, which is greater than 1. This signifies exponential growth. As the input 'x' increases, the output values will also increase without bound.

An exponential function f(x) = ab^{x} is always decreasing. What must be true about the value of its base, b?

A) b > 1

B) b < 0

C) 0 < b < 1

D) b = 1

Correct Answer: C

An exponential function is always decreasing when it represents exponential decay. This occurs when its base 'b' is a value between 0 and 1.

Which statement correctly describes a graphical feature of f(x) = ab^{x} where a > 0?

A) The graph is always concave down.

B) The graph is always concave up.

C) The graph is concave up for x > 0 and concave down for x < 0.

D) The concavity depends on the base b.

Correct Answer: B

The content states that exponential functions are 'always concave up or always concave down'. For the general form f(x) = ab^{x}, if the initial value 'a' is positive, the entire graph will be above the horizontal asymptote and will be concave up.