The rational function r is given by r(x) = $$\frac{x^2 + 4}{-3x^3 + 7}$$ . Which of the following describes the end behavior of r?

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

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

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

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

The rational function r is given by r(x) = (x-2)(x+4)/(x+2)(x+4). Which of the following statements about r is true?

Input values of r sufficiently close to -4 correspond to output values arbitrarily close to 3.

Input values of r sufficiently close to -4 correspond to output values arbitrarily close to 0.

Input values of r sufficiently close to -4 correspond to output values arbitrarily close to -3.

Input values of r sufficiently close to -4 correspond to output values that decrease without bound.

In the xy-plane, the graph of a rational function m has a hole at x = 1. Which of the following could define m(x)?

m(x) = $$\frac{(x-1)^2}{(x-4)(x-1)}$$

The rational function r is given by r(x) = ((x-1)(x+2))/((x-1)(x+3)). What is the domain of r?

all real number x where x ≠ -2, x ≠ 1

all real number x where x ≠ -2

Which of the following functions has a graph in the xy-plane with a vertical asymptote at x = 1 and a hole at x = -2?

h(x) = $$\frac{(x-1)(x+2)}{(x-1)^2(x+2)}$$

f(x) = $$\frac{(x-1)(x+2)^2}{(x+2)(x-3)}$$

g(x) = $$\frac{(x-1)(x+2)}{(x-1)(x+2)^2}$$

k(x) = $$\frac{(x-2)(x-3)}{(x-2)(x+1)}$$

Which of the following functions has a graph in the xy-plane with a vertical asymptote at x = 1 and a hole at x = -2?

h(x) = $$\frac{x^2 + 4x + 4}{x^2 + x - 2}$$

f(x) = $$\frac{x^2 - 4x + 3}{x^2 + x - 2}$$

g(x) = $$\frac{x^2 + x - 2}{x^2 + 3x + 2}$$

k(x) = $$\frac{x^2 + 4x + 3}{x^2 - x - 2}$$

The rational function r is given by r(x) = ((x - 4)(x + 3))/((x - 4)(x - 2)). Which of the following statements about the graph of r in the xy-plane is true?

The graph of r has a vertical asymptote at x = 2 and a hole at x = 4.

The graph of r has vertical asymptotes at x = -3 and x = 4.

The graph of r has vertical asymptotes at x = 2 and x = 4.

The graph of r has a vertical asymptote at x = 4 and a hole at x = 2.

The rational function $$h$$ is given by $$h(x) = \frac{(x + 2)^2(x - 3)^2}{(x + 2)(x - 3)^2}$$ . Which of the following statements about the graph of $$h$$ in the $$xy$$ -plane is true?

The graph of $$h$$ no real zeros, two holes, and no vertical asymptotes.

The graph of $$h$$ no real zeros, one hole, and one vertical asymptote.

The graph of $$h$$ one real zero, no holes, and one vertical asymptote.

The graph of $$h$$ no real zeros, no holes, and two vertical asymptotes.

Which of the following functions has a zero at $$x = 5$$ and has a graph in the $$xy$$ -plane with a vertical asymptote at $$x = -2$$ ?

h(x) = $$\frac{(x - 5)(x + 3)}{(x - 1)(x + 2)}$$

f(x) = $$\frac{(x + 5)(x - 1)}{(x - 2)(x + 3)}$$

g(x) = $$\frac{(x - 1)(x + 2)}{(x - 5)(x + 3)}$$

k(x) = $$\frac{(x - 5)^2(x + 2)}{(x - 5)(x + 2)^2}$$

The functions f and g are defined for all real numbers such that g(x) = f(2x) + 1. Which of the following sequences of transformations maps the graph of f to the graph of g in the xy-plane?

Horizontal compression by a factor of 1/2, then vertical shift up by 1 unit

Vertical shift down by 1 unit, then horizontal stretch by a factor of 2

Horizontal stretch by a factor of 2, then vertical shift down by 1 unit

Vertical shift up by 1 unit, then horizontal stretch by a factor of 1/2

The functions f and g are defined for all real numbers such that g(x) = -f(x+4). Which of the following sequences of transformations maps the graph of f to the graph of g in the xy-plane?

reflection of the graph f over the x-axis, followed by a horizontal translation of the graph of f by -4 units.

reflection of the graph f over the x-axis, followed by a horizontal translation of the graph of f by 4 units.

reflection of the graph f over the y-axis, followed by a horizontal translation of the graph of f by -4 units.

reflection of the graph f over the y-axis, followed by a horizontal translation of the graph of f by 4 units

The table shows values for a function h at selected values of x. Which of the following function types best models these data?

Quadratic, because these data demonstrate constant nonzero 2nd differences.

Linear, because these data demonstrate roughly constant rates of change.

Polynomial greater than degree 2, because these data demonstrate increasing, nonlinear rates of change.

Exponential, because there is a common ratio between consecutive terms.

The table shows values for a function f at selected values of x. Which of the following function types best models these data?

Cubic, because these data demonstrate constant nonzero 3rd differences.

Linear, because these data demonstrate roughly constant rates of change.

Quadratic, because these data demonstrate constant nonzero 2nd differences.

Polynomial greater than degree 3, because these data demonstrate increasing, linear 3rd differences.

An electronic bowling video game challenges players with an option to bowl with an increasing number of pins in each round. In the first round, a player bowls with the standard number of 10 pins. Then, the game adds an additional row of pins, as shown in the figure, so that round two includes 15 pins. For round three, another row of pins is added so that there are now 21 pins. Each round adds an additional row, and each additional row includes one more pin than the previous row. Which of the following statements and reasons is true?

The number of pins in a given round is best modeled by a quadratic function, because the differences between consecutive rows is constant.

The number of pins in a given round is best modeled by a linear function, because the differences between consecutive rows is linear.

The number of pins in a given round is best modeled by a quadratic function, because the differences between consecutive rows is linear.

The number of pins in a given round is best modeled by a linear function, because the differences between consecutive rows is constant.

AP PreCalculus Unit 1B MCQ Review AP Style

Authored by Michael Connolly

Mathematics

9th - 12th Grade

CCSS covered

Used 36+ times

AP PreCalculus Unit 1B MCQ Review AP Style

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This quiz focuses on rational functions and polynomial operations within AP Precalculus, specifically targeting 11th and 12th grade students. The problems comprehensively assess students' understanding of rational function behavior, including end behavior analysis, vertical and horizontal asymptotes, holes in graphs, domain determination, and zero identification. Students must demonstrate mastery of limit notation, polynomial division with remainders, binomial theorem applications, and function transformations involving dilations, translations, and reflections. Additionally, the quiz evaluates skills in analyzing data patterns to determine appropriate function models (linear, quadratic, exponential) and understanding how algebraic structures create graphical features. To succeed, students need strong algebraic manipulation skills, conceptual understanding of how numerator and denominator degrees affect rational function behavior, and the ability to connect symbolic representations to graphical characteristics. Created by Michael Connolly, a Mathematics teacher in US who teaches grade 9-12. This comprehensive assessment supports instruction by providing rigorous practice with AP-style multiple choice questions that mirror the format and complexity students will encounter on the actual AP Precalculus exam. The quiz serves effectively as a summative review tool following Unit 1B instruction, helping students consolidate their understanding of rational functions while identifying areas needing additional support. Teachers can deploy this assessment for formal review sessions, homework assignments, or formative evaluation before moving to subsequent units. The questions align with College Board standards for AP Precalculus, specifically addressing learning objectives related to rational function analysis, polynomial operations, function transformations, and mathematical modeling with appropriate function types.

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30 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

As the input values of r increase without bound, the output values of r decrease without bound.

As the input values of r increase without bound, the output values of r increase without bound.

As the input values of r increase without bound, the output values of r get arbitrarily close to 0.

As the input values of r increase without bound, the output values of r get arbitrarily close to 2.

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The rational function r is given by r(x) = (x + 2)/(x - 3). What are all intervals on which r(x) > 0?

(-2, 3) only

(-2, ∞)

(-∞, -3) ∪ (2, ∞)

(-∞, -2) ∪ (3, ∞)

Tags

CCSS.HSA.REI.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

x = 2 only

x = 0 and x = 2 only

x = 0 and x = 3 only

x = 0, x = 2, and x = 3

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

In the xy-plane, the graph of a rational function g has a vertical asymptote at x = 3. Which of the following could be an expression for g(x)?

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The rational function k is given by k(x) = (x - 2)/(x + 3). Which of the following limit statements about k is correct?

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The rational function r is given by r(x) = (x + 1)/(x - 4). Which of the following limit statements about r is correct?

Tags

CCSS.HSF-IF.C.7D

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