Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x^2$ + x$$

Question 4

What is the range of the quadratic function $$f(x) = -x^2$ + 4x + 5$$?

Accepted Answer

$$(-\infty, 9]$$

Question 5

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

Accepted Answer

$$(-3, -8)$$

Question 6

Which of the following is the correct solution set for $$f(x) = \frac{1}{2}x^2$ - 8 = 0$$?

Accepted Answer

$$x = \pm 4\sqrt{2}$$

Question 7

Which of the following rational functions has a vertical asymptote at $$x = 2$$?

Accepted Answer

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

Question 8

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

Accepted Answer

$$x = -3$$

Question 9

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

Accepted Answer

$$x = 4$$

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 of the following is the correct composition for $$g(f(x)) if$$ $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$?

Accepted Answer

$$g(f(x)) = \sqrt{x^2$} = |x|$$

Question 12

If $$f(x) = x^2$ - 3$$, what is the symmetry of $$f(x)$$?

Accepted Answer

Even

Question 13

Which of the following is the correct range for $$f(x) = |x| + x^2$?

Accepted Answer

$$[0, \infty)$$

Question 14

Given $$f(x) = x^4$ - 5x^2$ + 4 = 0$$, which of the following is NOT a root?

Accepted Answer

$$x = 3$$

Question 15

Which of the following statements about rational functions is true?

Accepted Answer

All rational functions have real-number coefficients and integer exponents.

Question 16

If $$f(x) = x^2$ + 4x + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(-2, 1)$$

Question 17

Which of the following is the correct solution set for $$f(x) = 2(x+3)^2$ - 8 = 0$$?

Accepted Answer

$$x = -3 \pm 2$$

Question 18

Which of the following is the correct equation for the slant asymptote of $$f(x) = \frac{x^2$ - 5x - 3}{x^2$ - x - 2}$$?

Accepted Answer

There is no slant asymptote.

Question 19

If the polynomial $$T(x) = -0.87x^3$ + 0.35x^2$ + 81.62x + 7684.94$$ models the number of thefts in thousands in the US after 1987, will this function be useful for modeling thefts over an extended period of time?

Accepted Answer

No, because higher-degree polynomials can produce unrealistic predictions outside the data range.

Precalculus Study Guide: Functions, Polynomials, Rational Functions, and Symmetry

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