Question 1

Which of the following is a polynomial function?

Accepted Answer

$$f(x) = x^3$ - 4x + 7$$

Question 2

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

Accepted Answer

Rises to the left and falls to the right

Question 3

Which statement best describes the graph of a polynomial function of degree 2 or higher?

Accepted Answer

It is smooth and continuous.

Question 4

If $$f(x) = (x - 2)^3$(x + 1)^2$, what are the zeros and their multiplicities?

Accepted Answer

$$x = 2 ($$multiplicity 3), $$x = -1 ($$multiplicity 2)

Question 5

A zero of a polynomial function has even multiplicity. What does the graph do at this zero?

Accepted Answer

It touches the x-axis and turns around.

Question 6

Use the Intermediate Value Theorem to determine if $$f(x) = x^3$ - 4x + 1$$ has a real zero between $$x = 1$$ and $$x = 2.$$

Accepted Answer

Yes, because $$f(1)$$ and $$f(2)$$ have opposite signs.

Question 7

What is the maximum number of turning points for a polynomial function of degree $$n$$?

Accepted Answer

$$n - 1$$

Question 8

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

Accepted Answer

$$-24$$

Question 9

Which of the following functions is symmetric about the y-axis?

Accepted Answer

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

Question 10

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

Accepted Answer

Degree 4, leading coefficient 1

Question 11

A chemical reaction rate is modeled by $$R(t) = -t^3$ + 6t^2$ - 9t + 2. $$What is the end behavior of $$R(t) as$$ $$t$$ increases without bound?

Accepted Answer

Falls to the right

Question 12

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

Accepted Answer

It has sharp corners.

Question 13

If $$f(x) = (x - 1)^4$(x + 2)$$, how does the graph behave at $$x = 1$$?

Accepted Answer

It touches the x-axis and turns around.

Question 14

A medical dosage model is given by $$D(x) = 5x^2$ - 20x + 15. $$What is the degree and leading coefficient?

Accepted Answer

Degree 2, leading coefficient 5

Question 15

If $$f(x) = -x^6$ + 3x^2$ - 2$$, what is the end behavior of the graph?

Accepted Answer

Falls to both left and right

Question 16

Which of the following is true about the zeros of $$f(x) = (x - 4)^2$(x + 1)^3$?

Accepted Answer

At $$x = 4$$, the graph touches the x-axis and turns around.

Question 17

A polynomial function $$f(x)$$ has degree 5 and a negative leading coefficient. What is the end behavior?

Accepted Answer

Falls to the left and rises to the right

Question 18

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which value is a zero of $$f(x)$$?

Accepted Answer

$$x = 1$$

Question 19

A polynomial $$f(x)$$ has a zero at $$x = 5$$ with multiplicity 3. What does the graph do at $$x = 5$$?

Accepted Answer

Crosses the x-axis and flattens out

Question 20

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

Accepted Answer

If $$f(a)$$ and $$f(b)$$ have opposite signs, there is at least one real root between $$a$$ and $$b.$$

Chapter 3: Polynomial Functions and Their Graphs – College Algebra Study Notes

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