Question 1

Which of the following best describes the function $$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_2$ x^2$ + a_1$ x + a_0$, where n$ is a nonnegative integer and a_n$$ 
eq 0$$?

Accepted Answer

A polynomial function

Question 2

Given the polynomial $$f(x) = 2x^3$ - 5x^2$ + 3x - 7$$, what is the degree of the polynomial?

Accepted Answer

$$3$$

Question 3

If $$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_0$ is a polynomial function, which coefficient must be nonzero?

Accepted Answer

$$a_n$$

Question 4

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = 2x$$^{-1}$$ + 5$$

Question 5

What is the leading term of the polynomial $$f(x) = -3x^4$ + 2x^3$ - x + 5$$?

Accepted Answer

$$-3x^4$$

Question 6

For the polynomial $$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_0$, what is the end behavior as x$$ 	o \infty$$ if n$ is even and a_n$$ \u003e 0$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 7

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

Accepted Answer

It is continuous and smooth everywhere.

Question 8

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the value of $$f(-x)$$?

Accepted Answer

$$x^4$$ - $$2x^2 + 1$

Question 9

Which of the following is the 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_1$ x + a_0$

Question 10

If $$f(x) = 2x^3$ - 5x^2$ + 3x - 7$$, what is $$f(2)$$?

Accepted Answer

$$-1$$

Precalculus Study Guide: Functions, Quadratics, and Polynomials

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