Question 1

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

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \cdots + a_1$ x + a_0$, where n$ is a nonnegative integer and a_n$$ 
eq 0$$

Question 2

A polynomial function $$f(x)$$ has a degree of 4 and a positive leading coefficient. What is the end behavior of its graph?

Accepted Answer

The graph rises to the left and rises to the right.

Question 3

Given the polynomial $$f(x) = (x+2)^2$(x-3)$$, which statement about its zeros and their multiplicities is correct?

Accepted Answer

$$x = -2 is a $$zero of multiplicity 2, and $$x = 3 is a $$zero of multiplicity 1.

Question 4

If a polynomial function $$f(x)$$ has a zero at $$x = 1$$ with multiplicity 3, what does the graph do at $$x = 1$$?

Accepted Answer

The graph crosses the x-axis at $$x = 1$$ and flattens out near the intercept.

Question 5

Which of the following best describes the Intermediate Value Theorem for polynomial functions?

Accepted Answer

If $$f(a)$$ and $$f(b)$$ have opposite signs, then there is at least one value $$c$$ between $$a$$ and $$b$$ for which $$f(c) = 0.$$

Question 6

A cubic polynomial $$f(x)$$ has a negative leading coefficient. What is the end behavior of its graph?

Accepted Answer

Falls to the right and rises to the left.

Question 7

Suppose $$f(x) = x^4$ - 5x^2$ + 4. $$How many turning points can the graph of $$f(x)$$ have at most?

Accepted Answer

$$3$$

Question 8

A real-world scenario: The height $$h(t) (in $$meters) of a projectile at time $$t (in $$seconds) is modeled by a polynomial function. If $$h(2) = 10$$ and $$h(3) = -5$$, what does the Intermediate Value Theorem guarantee?

Accepted Answer

There is a time $$c$$ between $$2$$ and $$3$$ when the projectile is at ground level ($$h(c) = 0).$$

Question 9

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

Accepted Answer

$$x = 4$$

Question 10

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

Accepted Answer

The graph can have sharp corners.

Question 11

If $$f(x) = (x-1)^2$(x+3)$$, what is the y-intercept of the graph?

Accepted Answer

$$f(0) = (-1)^2$ \cdot 3 = 3$$

Question 12

Which of the following polynomials has a graph that is symmetric about the y-axis?

Accepted Answer

$$f(x) = x^4$ - 2x^2$ + 1$$

Question 13

A polynomial function $$f(x)$$ has zeros at $$x = -1 ($$multiplicity 2) and $$x = 2 ($$multiplicity 3). Which statement is true?

Accepted Answer

The graph touches and turns around at $$x = -1$$ and crosses at $$x = 2.$$

Question 14

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

Accepted Answer

It has a vertical asymptote.

Question 15

If $$f(x) = -2x^5$ + 3x^2$ - 1$$, what is the end behavior of the graph?

Accepted Answer

Falls to the right and rises to the left.

Question 16

A polynomial function $$f(x) of $$degree 6 has at most how many turning points?

Accepted Answer

$$5$$

Question 17

Which of the following is a real-world application of finding the zeros of a polynomial function?

Accepted Answer

Determining when a company's profit will be zero based on a polynomial revenue model.

Question 18

If $$f(x) = x^2$(x-4)$$, what is the multiplicity of the zero at $$x = 0$$?

Accepted Answer

2

Question 19

Which of the following steps is NOT part of the five-step strategy for graphing polynomial functions?

Accepted Answer

Find the domain of the function.

Polynomial Functions and Their Graphs: Key Concepts and Graphing Strategies

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