Q: Which of the following is the correct end behavior for the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

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

Question 1

Which of the following is the correct end behavior for the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

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

Question 2

Given the polynomial $$g(x) = x^3$ + 2x^2$ - 5x - 6$$, which of the following statements is TRUE?

Accepted Answer

The graph has at most 2 turning points.

Question 3

A pharmaceutical company models the amount of a drug in the bloodstream by $$M(t) = 0.5t^4$ + 3.45t^3$ - 96.65t^2$ + 347.7t. $$What is the most appropriate domain for $$t in $$this context?

Accepted Answer

$$t \geq 0$$

Question 4

Which of the following is NOT a characteristic of the graph of a polynomial function?

Accepted Answer

It has sharp corners.

Question 5

If $$f(x) = (x-2)^3$(x+1)^2$$, what is the behavior of the graph at $$x = -1$?

Accepted Answer

The graph bounces off the x-axis.

Question 6

Which of the following is the correct factored form for a polynomial with real zeros at $$x = -2 ($$multiplicity 2), $$x = 1$$, and $$x = 3$$?

Accepted Answer

$$f(x) = (x+2)^2$(x-1)(x-3)$$

Question 7

A rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$ has which of the following characteristics?

Accepted Answer

Vertical asymptotes at $$x = 2$$ and $$x = -2$$

Question 8

Which of the following is the correct application of the Rational Zeros Theorem for $$f(x) = 2x^3$ - x^2$ - 18x + 9$$?

Accepted Answer

Possible rational zeros are $$\pm1, \pm3, \pm9, \pm\frac{1}{2}, \pm\frac{3}{2}, \pm\frac{9}{2}$$

Question 9

Given $$f(x) = \frac{2x+5}{2x-6}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 10

Which of the following best describes the solution set for the inequality $$x^2 + 6x - 16$$ \u003e 0$$?

Accepted Answer

$$(-\infty, -8) \cup (2, \infty)$$

Question 11

If $$f(x) = x^3$ - 3x^2$ - 6x + 8$$ and $$x = 1 is a $$zero, what is the quotient when $$f(x) is $$divided by $$x-1$$ using synthetic division?

Accepted Answer

$$x^2 - 2x - 8$

Question 12

Which of the following rational functions has a hole at $$x = 3$$?

Accepted Answer

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

Question 13

For the rational function $$f(x) = \frac{x-3}{x^2$ + x - 2}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 14

Which of the following is TRUE about the Fundamental Theorem of Algebra?

Accepted Answer

Every polynomial of degree $$n$$ has exactly $$n$$ complex zeros.

Question 15

A rational function $$f(x) = \frac{x^2$ + 2x + 1}{x + 2}$$ has which type of asymptote?

Accepted Answer

Oblique (slant) asymptote

Question 16

Which of the following is the correct interval notation for the solution to $$\frac{4x+8}{x-4} \leq 0$$?

Accepted Answer

$$(-\infty, -2] \cup (4, \infty)$$

Question 17

If $$f(x) = x^4$ - 16x^2$ - 40x - 25$$, and one zero is $$x = 5$$, which of the following must also be a zero if all coefficients are real?

Accepted Answer

$$x = -1$$

Question 18

Which of the following best describes the behavior of the graph of $$f(x) = -x^5$ + 2x^3$ - x^2$ + 4 as$$ $$x 	o \infty$$?

Accepted Answer

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

Polynomial and Rational Functions: College Algebra Study Guide

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