Question 1

Which of the following is the correct general form of a polynomial function of degree $$n$$?

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_2$ x^2$ + a_1$ x + a_0$

Question 2

Given the polynomial $$f(x) = -2x^4$ + 5x^3$ - x + 7$$, what is the end behavior of its graph?

Accepted Answer

Falls to the left and falls to the right

Question 3

Which of the following statements about the graph of a polynomial function is TRUE?

Accepted Answer

The graph is always smooth and continuous with no sharp corners or breaks.

Question 4

If $$f(x) = (x-1)^2$(x+3)$$, which statement best describes the behavior of the graph at $$x=1$$?

Accepted Answer

The graph touches the x-axis and turns around at $$x=1.$$

Question 5

A cubic polynomial $$f(x)$$ has a positive leading coefficient. Which of the following best describes its end behavior?

Accepted Answer

Falls to the left and rises to the right

Question 6

Given $$f(x) = x^3$ + 2x^2$ - 4x - 8$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 0$$

Question 7

If $$f(x) = -4\left(x + \frac{1}{2}\$$right)^2$$(x-5)^3$$, what is the multiplicity of the zero at $$x=5$?

Accepted Answer

3

Question 8

Suppose $$f(x) = 3x^3$ - 10x + 9. $$Using the Intermediate Value Theorem, which interval is guaranteed to contain a real zero?

Accepted Answer

$$[-3, -2]$$

Question 9

How many turning points can the graph of a degree 5 polynomial have at most?

Accepted Answer

4

Question 10

Given $$f(x) = 2(x+2)^2$(x-3)$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$-24$$

Question 11

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

Accepted Answer

Y-axis symmetry

Question 12

If $$f(x) = (x-2)^3$(x+1)$$, what happens to the graph at $$x=2$$?

Accepted Answer

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

Question 13

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

Accepted Answer

It has sharp corners.

Question 14

A real-world scenario: The height $$h (in $$meters) of a projectile at time $$t (in $$seconds) is modeled by $$h(t) = -5t^2$ + 20t + 1. $$What is the end behavior of this polynomial?

Accepted Answer

Falls to the left and falls to the right

Question 15

If $$f(x) = x^4$ - 3x^2$ + 2$$, how many $$x-$$intercepts can the graph have at most?

Accepted Answer

4

Question 16

Which of the following is a correct application of the Intermediate Value Theorem?

Accepted Answer

If $$f(a)  0$$, then $$f(x) = 0$$ has at least one real root between $$a$$ and $$b.$$

Question 17

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

Accepted Answer

$$x = 0$$

Question 18

If a polynomial function has degree $$n$$, what is the maximum number of $$x-$$intercepts it can have?

Accepted Answer

$$n$$

Question 19

Which of the following best describes the graph of $$f(x) = -x^6$ + 2x^4$ - x^2$ + 5 as$$ $$x 	o \infty$$?

Accepted Answer

Falls to $$-\infty$$

Polynomial Functions and Their Graphs: Study Guide

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