Question 1

What is the remainder when $$f(x) = 5x^5$ + 3x^4$ + 2x^2$ + x is $$divided by $$(x-1)(x+1)$$?

Accepted Answer

$$f(1) + f(-1) - 2f(0)$$

Question 2

Using the Remainder Theorem, what is the remainder when $$f(x) = 3x^5$ - 8x^4$ - 11x^3$ + 4x^2$ + 6 is $$divided by $$(x-3)$$?

Accepted Answer

$$f(3)$$

Question 3

Which of the following is a factor of $$f(x) = 3x^5$ - 8x^4$ - 11x^3$ + 4x^2$ + 6 if$$ $$f(2) = 0$$?

Accepted Answer

$$(x-2)$$

Question 4

Using Descartes' Rule of Signs, how many possible positive real zeros does $$f(x) = 5x^5$ + 3x^4$ + 2x^2$ + x - 5$$ have?

Accepted Answer

5

Question 5

What is the maximum number of turning points for $$f(x) = x^5$ - 2x^4$ + x^3$ + 5$$?

Accepted Answer

4

Question 6

Find the domain of the rational function $$R(x) = \frac{2-x}{x^2$}.$$

Accepted Answer

$$x 
eq 0$$

Question 7

What is the horizontal asymptote of $$f(x) = \frac{4x}{3x-9}$$?

Accepted Answer

$$y = \frac{4}{3}$$

Question 8

Find the vertical asymptote of $$f(x) = \frac{x}{x^2$+4}.$$

Accepted Answer

No vertical asymptote

Question 9

What is the $$y-$$intercept of $$f(x) = \frac{9x}{x-1}$$?

Accepted Answer

$$(0, 0)$$

Question 10

Which of the following is the correct graph for $$f(x) = \frac{x^2$ - 7}{x-2}$$?

Accepted Answer

A graph with a vertical asymptote at $$x=2$$ and a slant asymptote $$y=x+2$$

Question 11

Given the graph of $$f(x) = \frac{9x}{x-1}$$, what is the domain?

Accepted Answer

$$x 
eq 1$$

Question 12

For the rational function $$f(x) = \frac{12}{2x-3}$$, what is the $$x-$$value where the function is undefined?

Accepted Answer

$$x = \frac{3}{2}$$

Question 13

Which of the following describes the end behavior of $$f(x) = \frac{2x^2$}{x^2$+1} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 2$$

Question 14

If $$f(x) = \frac{x^2$-7}{x-2}$$, what is the slant (oblique) asymptote?

Accepted Answer

$$y = x + 2$$

Question 15

A chemical reaction rate is modeled by $$R(x) = \frac{4x}{3x-9}. $$What is the limiting rate as $$x$$ becomes very large?

Accepted Answer

The rate approaches $$\frac{4}{3}$$

Question 16

A population model is given by $$P(x) = \frac{2x}{x^2$+1}. $$What is the $$y-$$intercept?

Accepted Answer

$$(0, 0)$$

Question 17

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

Accepted Answer

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

Question 18

If $$f(x) = \frac{9x}{x-1}$$, what is the behavior of $$f(x) as$$ $$x$$ approaches $$1$$ from the right?

Accepted Answer

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

Question 19

A rational function $$f(x)$$ has a vertical asymptote at $$x=3$$ and a horizontal asymptote at $$y=2. $$Which of the following could be $$f(x)$$?

Accepted Answer

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

Study Guide: Polynomial and Rational Functions in College Algebra

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