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

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

Question 1

Given the polynomial function $$f(x) = x^3$ - 3x^2$ + x - 3$$, which of the following statements about its end behavior is correct?

Accepted Answer

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

Question 2

Which of the following is the correct set of $$x-$$intercepts for the function $$f(x) = (x-2)(x+1)(x-3)$$?

Accepted Answer

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

Question 3

A rational function $$f(x) = \frac{x^2$ + 1}{x-2}$$ has which of the following vertical asymptotes?

Accepted Answer

$$x = 2$$

Question 4

What is the horizontal asymptote of the function $$f(x) = \frac{2x^2$ + 3}{x^2$ - 1}$$?

Accepted Answer

$$y = 2$$

Question 5

Given $$f(x) = x^4$ - 16$$, which of the following is a correct factorization?

Accepted Answer

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

Question 6

For the polynomial $$f(x) = x^3$ - 4x$$, which of the following intervals is $$f(x)$$ positive?

Accepted Answer

$$(-2, 0) \cup (2, \infty)$$

Question 7

Which of the following best describes the end behavior of $$f(x) = -x^4$ + 2x^2$ - 1$$?

Accepted Answer

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

Question 8

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

Accepted Answer

$$x = 3, -3$$

Question 9

Which of the following is the correct domain for $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Question 10

Given the polynomial $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 11

Which of the following rational functions has a slant (oblique) asymptote?

Accepted Answer

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

Question 12

If $$f(x) = (x-1)^2$(x+2)$$, what is the multiplicity of the zero at $$x = 1$$?

Accepted Answer

2

Question 13

Which of the following best describes the graph of $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

Vertical asymptote at $$x = 2$$, horizontal asymptote at $$y = 0$$

Question 14

A polynomial $$f(x) of $$degree 4 with leading coefficient positive will have which end behavior?

Accepted Answer

Both ends up

Question 15

If $$f(x) = x^3$ - 4x$$, what are the $$x-$$intercepts?

Accepted Answer

Question 16

Given $$f(x) = \frac{x^2$ - 1}{x - 1}$$, what is the simplified form for $$x 
eq 1$$?

Accepted Answer

$$x + 1$$

Question 17

Which of the following is the correct factorization for $$x^3 - 8$?

Accepted Answer

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

Question 18

If $$f(x) = \frac{2x^2$ + 3x + 1}{x + 1}$$, what is the quotient when dividing $$2x^2 + 3x + 1$ by x + 1$?

Accepted Answer

$$2x + 1$$ with remainder $$0$$

Precalculus Exam 1A Study Guidance: Polynomial and Rational Functions

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