Q: Which of the following describes the end behavior of $$f(x) = -2x^6$ + 5x^2$ - 1$$?

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

Q: Given $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following statements is true about its end behavior?

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

Q: Which of the following best describes the end behavior of $$f(x) = 5x^3$ - 2x + 1$$?

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

Q: A chemical reaction's rate $$R (in $$mol/L·s) is modeled by $$R(t) = 0.5t^3$ - 2t^2$ + 3t$$, where $$t is $$time in seconds. What is the degree of this polynomial, and what does the leading term tell you about the long-term behavior of the rate?

Degree 3; as $$t \to \infty$$, $$R(t) \to \infty$$

Question 1

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$g(x) = x$$^{1/2}$$ + 4$$

Question 2

What is the degree and leading term of the polynomial $$f(x) = 3x^5$ - 2x^3$ + 4x - 8$$?

Accepted Answer

Degree: 5, Leading term: $$3x^5$$

Question 3

Which of the following describes the end behavior of $$f(x) = -2x^6$ + 5x^2$ - 1$$?

Accepted Answer

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

Question 4

Given $$f(x) = (x-2)^3$(x+1)^2$, which statement about the zeros is correct?

Accepted Answer

$$x = 2 is a $$zero of multiplicity 3; $$x = -1 is a $$zero of multiplicity 2

Question 5

A polynomial function $$f(x)$$ has real zeros at $$x = -3 ($$multiplicity 2), $$x = 0 ($$multiplicity 1), and $$x = 4 ($$multiplicity 3). Which of the following is a possible equation for $$f(x)$$?

Accepted Answer

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

Question 6

Which of the following graphs could NOT be the graph of a polynomial function?

Accepted Answer

A graph with a sharp corner at $$x = 1$$

Question 7

If a polynomial function $$f(x)$$ has degree $$n$$, what is the maximum number of turning points its graph can have?

Accepted Answer

$$n-1$$

Question 8

Which of the following is the standard form of the polynomial $$f(x) = -x^2$(x-3)^2$?

Accepted Answer

$$f(x) = -x^4$ + 6x^3$ - 9x^2$

Question 9

Suppose a polynomial function $$f(x)$$ has a real zero at $$x = 5 of $$even multiplicity. What does the graph of $$f(x) do at$$ $$x = 5$$?

Accepted Answer

It touches the x-axis at $$x = 5$$ and turns around

Question 10

Which of the following is a power function with an odd degree?

Accepted Answer

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

Question 11

A real-world scenario: The height $$h (in $$meters) of a projectile launched from the ground can be modeled by $$h(t) = -4.9t^2$ + 20t$$, where $$t is $$time in seconds. What type of function is this, and what is its degree?

Accepted Answer

Polynomial function, degree 2

Question 12

Given $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following statements is true about its end behavior?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

A polynomial function $$f(x)$$ has three real zeros: $$-2 ($$multiplicity 1), $$0 ($$multiplicity 2), and $$3 ($$multiplicity 1). What is the minimum possible degree of $$f(x)$$?

Accepted Answer

4

Question 15

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

Accepted Answer

The graph can have gaps or holes

Question 16

If $$f(x) = 2(x+1)(x-1)^2$(x-2)$$ and $$f(0) = 4$$, what is the value of the leading coefficient?

Accepted Answer

2

Question 17

Which of the following best describes the end behavior of $$f(x) = 5x^3$ - 2x + 1$$?

Accepted Answer

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

Question 18

A chemical reaction's rate $$R (in $$mol/L·s) is modeled by $$R(t) = 0.5t^3$ - 2t^2$ + 3t$$, where $$t is $$time in seconds. What is the degree of this polynomial, and what does the leading term tell you about the long-term behavior of the rate?

Accepted Answer

Degree 3; as $$t 	o \infty$$, $$R(t) 	o \infty$$

Section 5.1: Polynomial Functions – Definitions, Properties, and Identification

Study Guide - Practice Questions

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