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

Both ends go up as $$x \to \pm\infty$$

Question 1

Which of the following is a polynomial function?

Accepted Answer

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

Question 2

Given the polynomial $$f(x) = x^4$ + 4x^3$ + bx^2$ - 5x - 6$$, what is the degree of the polynomial?

Accepted Answer

$$4$$

Question 3

Which of the following describes the end behavior of $$f(x) = -2x^7$ + 5x^3$ - x$$?

Accepted Answer

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

Question 4

Which of the following is NOT a characteristic of a polynomial function?

Accepted Answer

The variable $$x$$ appears in the denominator.

Question 5

If $$r is a $$real zero of even multiplicity for a polynomial $$f(x)$$, what happens to the graph at $$x = r$$?

Accepted Answer

The graph turns around at $$x = r$$ and does not cross the $$x-$$axis.

Question 6

Find a polynomial of degree 3 whose real zeros are $$-3$$, $$2$$, and $$5.$$

Accepted Answer

$$f(x) = (x + 3)(x - 2)(x - 5)$$

Question 7

Which transformation is applied to the graph of $$f(x) = x^2$ to obtain g(x) = (x$$ - $$1)^2$$?

Accepted Answer

Shift right by 1 unit

Question 8

Given $$f(x) = 5x^2$(x + 2)\left(x - \frac{3}{2}\$$right)^4$$, what is the multiplicity of the zero x = -2$?

Accepted Answer

$$1$$

Question 9

Which of the following graphs best represents the function $$f(x) = x^4$ - 2x^2$?

Accepted Answer

A graph with two local minima and one local maximum, symmetric about the $$y-$$axis

Question 10

If $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$, what is the leading coefficient?

Accepted Answer

$$a_n$$

Question 11

Which of the following statements is true about the graph of $$f(x) = x^3$?

Accepted Answer

It is symmetric about the origin.

Question 12

A polynomial function $$f(x)$$ has zeros at $$x = 1 ($$multiplicity 2) and $$x = -2 ($$multiplicity 1). Which of the following could be its equation?

Accepted Answer

$$f(x) = (x - 1)^2$(x + 2)$$

Question 13

Which of the following is the range of $$f(x) = x^4$?

Accepted Answer

$$[0, \infty)$$

Question 14

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

Accepted Answer

$$3$$

Question 15

Which of the following is equivalent to saying $$r is a $$real zero of a polynomial $$f(x)$$?

Accepted Answer

$$f(r) = 0$$

Question 16

Which of the following is a power function?

Accepted Answer

$$f(x) = x^6$

Question 17

Which of the following is the domain of $$f(x) = x^2$ - 1$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 18

If $$f(x) = (x - 2)^3$, what is the behavior of the graph at x = 2$?

Accepted Answer

The graph crosses the $$x-$$axis and flattens at $$x = 2.$$

Question 19

Which of the following is the correct end behavior for $$f(x) = x^6$ - 2x^4$ + 3$$?

Accepted Answer

Both ends go up as $$x 	o \pm\infty$$

Polynomial Functions: Definitions, Properties, Graphs, and Zeros

Study Guide - Practice Questions