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

As $$x \to \pm\infty$$, $$f(x) \to \infty$$

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 $$x 	o \pm\infty$$, $$f(x) 	o \infty$$

Question 4

For the polynomial $$h(x) = x^3$ - 2x^2$ - 3x + 6$$, which of the following is a zero?

Accepted Answer

$$x = 2$$

Question 5

Given $$f(x) = x^4$ - 2x^2$ + 3x - 4$$, what is the maximum number of turning points the graph of $$f(x)$$ can have?

Accepted Answer

$$3$$

Question 6

A polynomial $$p(x) of $$degree 5 with rational coefficients has zeros $$-2 + i$$, $$1 + \sqrt{3}$$, and $$3. $$Which of the following is NOT necessarily a zero of $$p(x)$$?

Accepted Answer

$$-3$$

Question 7

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 8

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

Accepted Answer

$$y = 3$$

Question 9

Given $$f(x) = x^3$ - 2x^2$ - 3x + 6$$, use synthetic division to divide by $$(x-2). $$What is the remainder?

Accepted Answer

$$0$$

Question 10

Which of the following is the correct factored form for a cubic polynomial with $$x-$$intercepts at $$x=1$$, $$x=-2$$, and $$x=3$$, and $$p(x) 	o -\infty as$$ $$x 	o \infty$$?

Accepted Answer

$$-a(x-1)(x+2)(x-3)$$,\ a\u003e0$

Question 11

For the function $$f(x) = \frac{x-1}{(x-5)(x+1)}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 5$$ and $$x = -1$$

Question 12

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

Accepted Answer

$$(0, 2)$$

Question 13

If $$f(x) = x^4$ - 2x^2$ + 3x - 4$$, what is the maximum number of $$x-$$intercepts the function can have?

Accepted Answer

$$4$$

Question 14

Which of the following is true about the zeros of $$p(x) = x^5$ + 2x^4$ + x^3$ + 3x^2$ + 2x + 1 if$$ $$-2 + i is a $$zero?

Accepted Answer

$$-2 - i is $$also a zero

Question 15

Given $$f(x) = x^3$ - 2x^2$ - 3x + 6$$, which of the following is the correct list of all zeros?

Accepted Answer

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

Question 16

For the rational function $$f(x) = \frac{x-10}{x^2$ - 4x - 5}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 2)$$

Question 17

Which of the following intervals describes where $$f(x) = x^3$ - 2x^2$ - 3x + 6 is $$positive?

Accepted Answer

$$(-\infty, -1) \cup (2, 3)$$

Question 18

Which of the following is the correct equation for a polynomial of degree 5 with zeros $$-2 + i$$, $$-2 - i$$, $$1 + \sqrt{3}$$, $$1 - \sqrt{3}$$, and $$3$$?

Accepted Answer

$$(x - 3)[(x + 2)^2$ + 1][(x - 1)^2$ - 3]$$

Question 19

For the function $$f(x) = x^4$ - 2x^2$ + 3x - 4$$, which of the following is the sign of the leading coefficient?

Accepted Answer

Positive

Polynomials and Rational Functions: Structure, Zeros, Graphs, and Asymptotes

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