$$f(x) = a(x + 2)(x - 3)(x + 1)$$, where $$a \neq 0$$

$$f(x) \to +\infty as$$ $$x \to \pm\infty$$

Question 1

Which of the following functions is a polynomial function?

Accepted Answer

$$f(x) = 3x - 1 - 2x^5$

Question 2

What is the degree of the polynomial $$h(x) = x$$^{12}$$ + 3x^2$ - 10x$$?

Accepted Answer

$$12$$

Question 3

Given the polynomial $$f(x) = 2(x + 3)^2$(x + 2)^3$(x - 5)$$, what is the multiplicity of the zero at $$x = 2$$?

Accepted Answer

$$3$$

Question 4

For the polynomial $$f(x) = -6(x - 3)^2$(x + 3)^3$(x - 4)$$, what is the end behavior as $$x 	o -\infty$$?

Accepted Answer

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

Question 5

Which of the following is the standard form of the polynomial $$h(x) = 4x^2$ - 5x + 2x - 4$$?

Accepted Answer

$$h(x) = 4x^2$ - 3x - 4$$

Question 6

What is the domain of the rational function $$f(x) = \frac{1}{x^2$ - 2x - 8}$$?

Accepted Answer

$$x 
eq 2, x 
eq -4$$

Question 7

If a polynomial function has degree $$n$$, what is the greatest number of turning points it can have?

Accepted Answer

$$n - 1$$

Question 8

Given the polynomial $$f(x) = x^3$(x - 2)^2$(x + 1)$$, which zero will the graph touch but not cross the x-axis?

Accepted Answer

$$x = 2$$

Question 9

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

Accepted Answer

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

Question 10

Which of the following is NOT a property of polynomial functions?

Accepted Answer

The graph can have holes or gaps.

Question 11

Find the domain of the rational function $$f(x) = \frac{x^2$}{x^2$ + 1}.$$

Accepted Answer

All real numbers

Question 12

Given the zeros $$-2, 3, -1$$ and degree $$3$$, which of the following is a possible polynomial function?

Accepted Answer

$$f(x) = a(x + 2)(x - 3)(x + 1)$$, where $$a 
eq 0$$

Question 13

For the rational function $$f(x) = \frac{x - 2}{x^2$ + 3x - 10}$$, which value is NOT in the domain?

Accepted Answer

$$x = -5$$

Question 14

If $$f(x) = a_nx^n + \ldots + a_0$ and a_n$$ \u003e 0$$, n$ is even, what is the end behavior of f(x$$)$$?

Accepted Answer

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

Question 15

Which of the following is the correct definition of a rational function?

Accepted Answer

A function that can be written as $$f(x) = \frac{p(x)}{q(x)}$$, where $$p(x)$$ and $$q(x)$$ are polynomials and $$q(x) 
eq 0.$$

Question 16

If $$f(x) = (x - 1)^3$(x + 2)^2$, what is the degree of the polynomial?

Accepted Answer

$$5$$

Question 17

Which of the following describes the behavior of the graph at a zero with even multiplicity?

Accepted Answer

The graph touches the x-axis and turns around.

Question 18

Given the polynomial $$f(x) = 2x^4$(x - 1)(x + 5)$$, what is the leading term?

Accepted Answer

$$2x^6$$

Question 19

Which of the following is the constant term in the polynomial $$f(x) = 3x^4$ - 2x^2$ + 7x - 5$$?

Accepted Answer

$$-5$$

Polynomial and Rational Functions: Definitions, Properties, and Graphing

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