Question 1

Which of the following statements about the function $$f(x) = \frac{1}{x} is $$true?

Accepted Answer

It is an odd function because $$f(-x) = -f(x)$$ for all $$x 
eq 0.$$

Question 2

Given the polynomial $$f(x) = 5x^4$ + 3x^3$ - (x-1)(x^2$-2x)$$, which of the following is the correct expanded form?

Accepted Answer

$$5x^4$$ + $$3x^3$$ - $$x^3$$ + $$3x^2 - 2x$

Question 3

Which of the following functions is neither even nor odd?

Accepted Answer

$$g(x) = |x| + x^2$

Question 4

The range of all polynomial functions is:

Accepted Answer

Depends on the degree and leading coefficient of the polynomial

Question 5

If $$f(x) = 2(x+3)^2$ - 8$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, -8)$$

Question 6

Given $$f(x) = -x^2$ + 4x + 5$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 9]$$

Question 7

Which of the following is a rational function?

Accepted Answer

$$g(x) = \frac{3x}{x-4}$$

Question 8

For the rational function $$r(x) = \frac{3x}{x-4}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 9

If $$f(x) = x^4$ - 5x^2$ + 4 = 0$$ and $$x = 2$$ and $$x = -2$$ are roots, what is the complete solution set?

Accepted Answer

$$\{-2, -1, 1, 2\}$$

Question 10

Which of the following describes the end behavior of $$f(x) = -2x^3$ - 3x + 4 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 11

Which statement is true about the graph of $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

It has vertical asymptotes at $$x = 2$$ and $$x = -2.$$

Question 12

If $$f(x) = x^2$ - 13x + 6$$ and $$x + 3 is a $$known factor, which of the following is a root of $$f(x)$$?

Accepted Answer

$$x = -3$$

Question 13

Which of the following best describes the solution set to $$f(x) = \frac{1}{2}x^2$ - 8 = 0$$?

Accepted Answer

$$x = \pm 4$$

Question 14

Which of the following is the correct definition of a rational function?

Accepted Answer

A function that can be written as the ratio of two polynomials.

Question 15

Given $$f(x) = x^3$ - 3x^2$ + 2x$$, what is the multiplicity of the root $$x = 1$$?

Accepted Answer

1

Question 16

Which of the following is true about the graph of $$f(x) = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 17

If $$f(x) = x^2$ + 1$$ and $$g(x) = x^2$ - 1$$, which of the following is $$f(x) - g(x)$$?

Accepted Answer

$$2$$

Question 18

Which of the following is the correct order of roots for $$f(x) = (x-1)(x+2)(x-3)$$ from smallest to largest?

Accepted Answer

$$x = -2, x = 1, x = 3$$

Question 19

A polynomial function $$P(x)$$ models the number of thefts in the US after 1987. Which of the following is a limitation of using this model for an extended period of time?

Accepted Answer

Polynomial models may not accurately predict long-term trends due to changing real-world factors.

Precalculus Study Guide: Functions, Polynomials, and Rational Functions

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