AP®MathsCollege BoardPrecalculusExam QuestionsPolynomial & Rational FunctionsLinear, Quadratic & Polynomial Functions

Linear, Quadratic & Polynomial Functions (College Board AP® Precalculus): Exam Questions

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Linear, Quadratic & Polynomial Functions

1
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1 mark

A polynomial function q is given by q open parentheses x close parentheses equals x open parentheses x minus 5 close parentheses open parentheses x plus 3 close parentheses. What are all intervals on which q open parentheses x close parentheses less or equal than 0 ?

  • \left[0 , 5\right]

  • \left[- 3 , 5\right]

  • \left(- \infty , - 3\right] \cup \left[0 , 5\right]

  • \left[- 3 , 0\right] \cup \left[5 , \infty\right)

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2
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1 mark

The function g is given by g \left(x\right) = - 3 x^{5} + 4 x^{2} - 1. Which of the following describes the end behavior of g ?

  • \underset{x \rightarrow - \infty}{\lim} g \left(x\right) = - \infty and \underset{x \rightarrow \infty}{\lim} g \left(x\right) = - \infty

  • \underset{x \rightarrow - \infty}{\lim} g \left(x\right) = \infty and \underset{x \rightarrow \infty}{\lim} g \left(x\right) = \infty

  • \underset{x \rightarrow - \infty}{\lim} g \left(x\right) = - \infty and \underset{x \rightarrow \infty}{\lim} g \left(x\right) = \infty

  • \underset{x \rightarrow - \infty}{\lim} g \left(x\right) = \infty and \underset{x \rightarrow \infty}{\lim} g \left(x\right) = - \infty

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3
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1 mark

The polynomial function p is given by p \left(x\right) = \left(x - 2\right) \left(x^{2} + x + 7\right). Which of the following describes the zeros of p ?

  • p has exactly three distinct real zeros.

  • p has exactly two distinct real zeros.

  • p has exactly one distinct real zero and no non-real zeros.

  • p has exactly one distinct real zero and two non-real zeros.

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4
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1 mark

The table shows values for a function h at selected values of x.

x

0

1

2

3

4

h \left(x\right)

12

40

62

78

88

Which of the following claim and explanation statements best fits these data?

  • h is best modeled by a linear function, because the rate of change over consecutive equal-length input-value intervals is constant.

  • h is best modeled by a linear function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

  • h is best modeled by a quadratic function, because the rate of change over consecutive equal-length input-value intervals is constant.

  • h is best modeled by a quadratic function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

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5
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1 mark

The polynomial function k is given by k \left(x\right) = a x^{4} - b x^{3} + 21, where a and b are nonzero real constants. Each of the zeros of k has multiplicity 1. In the x y-plane, an x-intercept of the graph of k is open parentheses 12.458 comma space 0 close parentheses. A zero of k is - 1.23 - 0.56 i. Which of the following statements must be true?

  • The graph of k has three x-intercepts.

  • - 1.23 + 0.56 i is a zero of k.

  • The equation k \left(x\right) = 0 has four real solutions.

  • The graph of k is tangent to the x-axis at x = 12.458.

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6
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1 mark

The number of visitors entering a theme park on a particular day is modeled by the function V, where V \left(t\right) = 0.05 t^{3} - 1.2 t^{2} + 8.1 t + 2.5 for 0 \leq t \leq 16. V \left(t\right) is measured in hundreds of visitors per hour, and t is measured in hours since the park opened. Based on the model, at what value of t does the rate of visitors entering the park change from increasing to decreasing?

  • t = 16

  • t = 11.162

  • t = 4.838

  • t = 2.500

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