Q: If $$g(x) = x^3$ - 2x^2$, which of the following describes the end behavior of g(x$$)$$?

As $$x \to \infty$$, $$g(x) \to \infty$$; as $$x \to -\infty$$, $$g(x) \to -\infty.$$

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 $$f(x) = 2x^3$ + x^2$ - 13x + 6$$, and knowing that $$x + 3 is a $$factor, which of the following is a solution to $$f(x) = 0$$?

Accepted Answer

$$x = -3$$

Question 3

Which of the following best describes the range of the quadratic function $$f(x) = -x^2$ + 4x + 5$$?

Accepted Answer

$$(-\infty, 9]$$

Question 4

For the rational function $$r(x) = \frac{3x}{x-4}$$, which of the following statements is true?

Accepted Answer

There is a vertical asymptote at $$x = 4.$$

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 4$$

Question 6

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

Accepted Answer

$$(-3, -8)$$

Question 7

If $$g(x) = x^3$ - 2x^2$, which of the following describes the end behavior of g(x$$)$$?

Accepted Answer

As $$x 	o \infty$$, $$g(x) 	o \infty$$; as $$x 	o -\infty$$, $$g(x) 	o -\infty.$$

Question 8

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

Accepted Answer

$$x = -3 \pm 2$$

Question 9

Which of the following is a correct statement about the symmetry of $$f(x) = |x| + x^2$?

Accepted Answer

It is an even function.

Question 10

Given the rational function $$f(x) = \frac{x^2$ - 5x - 3}{x^2$ - x - 12}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = 4$$

Question 11

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

Accepted Answer

$$[-8, \infty)$$

Question 12

If $$f(x) = x^4$ - 5x^2$ + 4 = 0$$ and $$x = 2$$ and $$x = -2$$ are roots, which of the following is a factor of $$f(x)$$?

Accepted Answer

$$(x^2 - 4$$)$$

Question 13

Which of the following describes the behavior of the graph of $$f(x) = (x - 2)^2$(x + 1) at$$ $$x = 2$$?

Accepted Answer

The graph touches and turns at $$x = 2.$$

Question 14

Which of the following is the correct solution set for $$f(x) = -x^2$ + 4x + 5 = 0$$?

Accepted Answer

$$x = 5, x = -1$$

Question 15

Which of the following is the correct horizontal asymptote for $$f(x) = \frac{x^3$}{x^2$ - 1}$$?

Accepted Answer

None; there is a slant asymptote.

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 range for $$f(x) = x^2$ + 4x + 5$$?

Accepted Answer

$$[1, \infty)$$

Question 18

Which of the following is the correct solution set for $$f(x) = x^2$ + 4x + 5 = 0$$?

Accepted Answer

No real solutions

Question 19

If the polynomial function $$T(x) = -0.873x^3$ + 0.35x^2$ + 81.62x + 7684.94$$ models the number of thefts, $$T(x)$$, in thousands in the United States $$x$$ years after 1987, which of the following is a valid concern about using this model for long-term predictions?

Accepted Answer

The model may not be accurate for years far beyond 1987 due to changing social and economic factors.

Precalculus Study Guide: Functions, Polynomials, and Rational Functions

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