The function $$f$$ is given by $$f(x) = 4 \left( \frac{2}{3} \right)^x$$ . Which of the following describes the end behavior of $$f$$ ?

$$\lim_{x \to -\infty} f(x) = \infty$$ and $$\lim_{x \to \infty} f(x) = 0$$

$$\lim_{x \to -\infty} f(x) = \infty$$ and $$\lim_{x \to \infty} f(x) = \infty$$

$$\lim_{x \to -\infty} f(x) = \infty$$ and $$\lim_{x \to \infty} f(x) = -\infty$$

$$\lim_{x \to -\infty} f(x) = 0$$ and $$\lim_{x \to \infty} f(x) = \infty$$

The function g is given by g(x) = $$2(3)^x$$ . Which of the following describes the end behavior of g?

$$\lim_{x \to -\infty} g(x) = 0$$ and $$\lim_{x \to \infty} g(x) = \infty$$

$$\lim_{x \to -\infty} g(x) = -\infty$$ and $$\lim_{x \to \infty} g(x) = 0$$

$$\lim_{x \to -\infty} g(x) = 0$$ and $$\lim_{x\to\infty}g(x)=-\infty$$

$$\lim_{x \to -\infty} g(x) = \infty$$ and $$\lim_{x \to \infty} g(x) = 0$$

The exponential function h is defined by h(x) = ab^x, where a and b are positive constants. The table gives values of $$h(x) = ab^x$$ at selected values of x. Which of the following statements is true?

h demonstrates exponential growth because a > 0 and b > 1.

h demonstrates exponential decay because a > 0 and 0

h demonstrates exponential decay because a > 0 and b > 1.

h demonstrates exponential growth because a > 0 and 0

The exponential function f is defined by f(x) = $$ab^x$$ , where a and b are positive constants. The table gives values of f(x) at selected values of x. Which of the following statements is true?

f demonstrates exponential decay because a > 0 and 0

f demonstrates exponential decay because a > 0 and b > 1.

f demonstrates exponential growth because a > 0 and 0

f demonstrates exponential growth because a > 0 and b > 1.

Which of the following statements is true about the exponential function $$f$$ given by $$f(x) = 4\left(\frac{1}{3}\right)^x$$ ?

f is always decreasing, and the graph of f is always concave up.

f is always increasing, and the graph of f is always concave up.

f is always increasing, and the graph of f is always concave down.

f is always decreasing, and the graph of f is always concave down.

Which of the following statements is true about the exponential function $$g$$ given by $$g(x) = \frac{1}{2} \cdot 3^x$$ ?

g is always increasing, and the graph of g is always concave up.

g is always increasing, and the graph of g is always concave down.

g is always decreasing, and the graph of g is always concave up.

g is always decreasing, and the graph of g is always concave down.

Which of the following statements is true about the exponential function $$f$$ given by $$f(x) = 7 \left( \frac{4}{5} \right)^x$$ ?

(C) $$f$$ is decreasing at an increasing rate.

(A) $$f$$ is increasing at an increasing rate.

(B) $$f$$ is increasing at a decreasing rate.

(D) $$f$$ is decreasing at a decreasing rate.

The figure shows a portion of the graph of a function h. Which of the following conclusions is possible for h?

h is exponential because the output values are proportional over equal-length input-value intervals.

h is logarithmic because the output values are proportional over equal-length input-value intervals.

h is logarithmic because the output values are proportional over equal-length output-value intervals.

h is exponential because the output values are proportional over equal-length output-value intervals.

In the xy-plane, the function f, given by f(x) = $$4^{(x-2)}$$ , is a horizontal translation of the exponential function g, given by g(x) = $$4^x$$ . Which of the following is an equivalent form for f(x) that expresses f as a vertical dilation of g?

f(x) = $$\frac{1}{16} \cdot 4^x$$

A linear regression was used to create a model for a set of data. The figure shows a graph of the residuals of the linear regression. Which of the following statements about the linear regression is true?

linear regression model is not appropriate, because the residuals show a clear pattern

linear regression model is appropriate, because the residuals show a clear pattern

linear regression model is appropriate, but a quadratic regression may be a better model

linear regression model is not appropriate, because the residuals do not show a linear pattern

A regression model was created for the data in the graph above (left). The residual plot for the model is given above (right). Which of the following statements about the regression model is best?

quadratic regression model was used and the model is not appropriate.

quadratic regression model was used and the model is appropriate.

exponential regression model was used and the model is appropriate.

exponential regression model was used and the model is not appropriate.

Mr. Passwater believed a set of data displayed exponential growth. He used the set of data to create an exponential regression model. The residual plot for his model is shown above. Based on the residual plot above, which of the following conclusions is correct?

The residual plot has no apparent pattern, so the exponential model was appropriate.

The residual plot has no apparent pattern, so the exponential model was not appropriate.

The residual plot displays a pattern, so the exponential model was appropriate.

The residual plot displays a pattern, so the exponential model was not appropriate.

The function $$h$$ is increasing for all values of $$x$$ , and the graph of $$h$$ is concave up for all values of $$x$$ . Let the function $$k$$ be the inverse of $$h$$ . Which of the following statements about $$k$$ is true?

(B) $$k$$ is increasing, and the graph of $$k$$ is concave down.

(A) $$k$$ is increasing, and the graph of $$k$$ is concave up.

The function g is given by g(x) = log_3(x - 4). Which of the following statements about the construction of the inverse of g is true?

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has domain of real values of x.

The inverse of g cannot be constructed because the graph of g is not defined for all real values of x.

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has domain x > 4.

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has range of real values of y.

AP PreCalculus Unit 2A MCQ Review AP Style Questions

Authored by Michael Connolly

Mathematics

9th - 12th Grade

CCSS covered

Used 81+ times

AP PreCalculus Unit 2A MCQ Review AP Style Questions

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This AP PreCalculus quiz focuses on sequences, exponential functions, and function composition and inverses. The material is designed for grade 11-12 students taking Advanced Placement PreCalculus, covering sophisticated topics that bridge algebra and calculus. Students need strong algebraic manipulation skills to work with geometric and arithmetic sequences, finding nth terms and identifying sequence types from graphs and tables. They must understand exponential function behavior, including end behavior analysis using limits, distinguishing between growth and decay, and recognizing concavity patterns. The quiz requires mastery of exponential function transformations, including horizontal and vertical translations and dilations, as well as rewriting exponential expressions in equivalent forms. Students also need to evaluate function composition problems, work with inverse functions, analyze residual plots to determine model appropriateness, and apply exponential models to real-world contexts like traffic patterns. Created by Michael Connolly, a Mathematics teacher in US who teaches grade 9-12. This comprehensive review quiz serves multiple instructional purposes in the AP PreCalculus classroom, functioning effectively as a unit review, practice assessment, or homework assignment to reinforce Unit 2A concepts. The AP-style multiple choice format prepares students for the rigor and question types they will encounter on the actual AP exam, while the diverse problem set allows teachers to identify areas where students need additional support. This quiz works particularly well as a formative assessment tool, helping instructors gauge student understanding before moving to more advanced topics or as a warm-up activity to activate prior knowledge. The problems align with College Board standards for AP PreCalculus, specifically addressing learning objectives related to sequences and series (LO 1.1A-1.1C), exponential functions and their properties (LO 2.1A-2.1E), function transformations (LO 2.2A-2.2C), function composition (LO 3.1A), and inverse functions (LO 3.2A-3.2B).

Content View

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39 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Values of the terms of a geometric sequence g_n are graphed in the figure. Which of the following is an expression for the nth term of the geometric sequence?

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Values of the terms of a geometric sequence are graphed in the figure. Which of the following is an expression for the nth term of the geometric sequence?

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Values of the terms of a geometric sequence g_n are graphed in the figure. Which of the following is an expression for the nth term of the geometric sequence?

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Let a_n represent an arithmetic sequence where a_3 = 22 and a_6 = 10. What is the value of a_{12}?

-48

-14

-4

-2

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The table gives values of the sequence S_n at selected values of n. Which of the following statements about S_n is true?

S_n could be an arithmetic sequence, because successive terms have a constant difference.

S_n could be an arithmetic sequence, because successive terms have constant proportional change.

S_n could be a geometric sequence, because successive terms have a constant difference.

S_n could be a geometric sequence, because successive terms have constant proportional change.

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The table gives values of the sequence s_n at selected values of n. Which of the following statements about s_n is true?

s_n could be an arithmetic sequence, because successive terms have a constant difference.

s_n could be an arithmetic sequence, because successive terms have constant proportional change.

s_n could be a geometric sequence, because successive terms have a constant difference.

s_n could be a geometric sequence, because successive terms have constant proportional change.

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Let g_n be a geometric sequence with g_1 = 3 and g_4 = 24. Which of the following is the value of g_3?

Tags

CCSS.HSF.BF.A.2

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