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

Question 1

Given the polynomial $$g(x) = 6x^4$ - \frac{1}{2}x^2$ + 7$$, what is the leading term?

Accepted Answer

$$6x^4$$

Question 2

What is the degree of the polynomial $$g(x) = 6x^4$ - \frac{1}{2}x^2$ + 7$$?

Accepted Answer

$$4$$

Question 3

Which of the following best describes the end behavior of $$f(x) = 5x^4$ - \frac{1}{3}x^2$ - 4$$?

Accepted Answer

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

Question 4

For the function $$f(x) = x^3$ - x^2$ - 2x + 22$$, is $$x = 2 a $$zero of the function?

Accepted Answer

No

Question 5

Which of the following is the correct factorization of $$x^3$$ - $$2x^2 + x$?

Accepted Answer

$$x(x-1)(x-2)$$

Question 6

Given $$f(x) = x^4$ - 6x^2$ + 3x$$, what is the maximum number of real zeros the function can have?

Accepted Answer

$$4$$

Question 7

For the polynomial $$h(x) = x^4$ + 2x^3$ - 3x^2$ - 7x + 1$$, which of the following numbers is NOT a zero?

Accepted Answer

$$-2$$

Question 8

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

Accepted Answer

$$y = 3$$

Question 9

Which of the following describes the domain of $$f(x) = \frac{x-10}{x^2$ - 4x - 5}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, 5) \cup (5, \infty)$$

Question 10

If $$f(x) = x^3$ - 2x^2$ + x$$, what is the multiplicity of the zero $$x = 0$$?

Accepted Answer

$$1$$

Question 11

Which of the following is the correct inverse of the function $$f(x) = -3x - 2$$?

Accepted Answer

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

Question 12

For the polynomial $$p(x) = x^4$ - 6x^2$ + 3x$$, what is the maximum number of turning points?

Accepted Answer

$$3$$

Question 13

Which of the following is a vertical asymptote of $$f(x) = \frac{x-1}{(x-5)(x+1)}$$?

Accepted Answer

$$x = -1$$

Question 14

Given $$f(x) = x^3$ - 2x^2$ + x$$, which of the following is a $$y-$$intercept?

Accepted Answer

$$(0, 0)$$

Question 15

Which of the following best describes the range of $$f(x) = \frac{x-1}{(x-5)(x+1)}$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 16

If $$f(x) = x^4$ - 6x^2$ + 3x$$, what is the sign of $$f(x)$$ for $$x \u003e 2$$?

Accepted Answer

Always positive

Question 17

Which of the following is the correct quotient when $$x^4$$ + $$5x^2 - 4x + 13$ is divided by x + 3$ using synthetic division?

Accepted Answer

$$x^3$$ + $$3x^2 + 14x - 55$

Question 18

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

Accepted Answer

$$(-\frac{2}{3}, 0)$$

Question 19

For the polynomial $$h(x) = x^4$ + 2x^3$ - 3x^2$ - 7x + 1$$, what is the leading coefficient?

Accepted Answer

$$1$$

Question 20

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

Accepted Answer

Both ends down

Polynomial and Rational Functions: Structure, Graphs, and Analysis

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