Q: What is the end behavior of the function $$f(x) = -3x^4$ + 2x^3$ - 5x + 7$$?

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

Q: If the leading coefficient of a polynomial of even degree is positive, what is the end behavior of the graph?

Both ends go up as $$x \to \infty$$ and $$x \to -\infty.$$

Q: A polynomial function $$f(x)$$ has degree 4 and a negative leading coefficient. What is the end behavior of $$f(x)$$?

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

Question 1

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

Accepted Answer

A graph with a hole or discontinuity.

Question 2

Given the polynomial $$f(x) = (x-2)^2$(x+1)$$, what is the multiplicity of the zero at $$x=2$$?

Accepted Answer

$$2$$

Question 3

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 4

Which of the following is always true about the graph of a polynomial function?

Accepted Answer

The degree is greater than the number of turning points.

Question 5

What is the end behavior of the function $$f(x) = -3x^4$ + 2x^3$ - 5x + 7$$?

Accepted Answer

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

Question 6

If $$f(x) = (x-1)^2$(x+3)$$, which of the following statements is true?

Accepted Answer

$$x=1 is a $$zero of multiplicity 2 and the graph touches the x-axis at $$x=1.$$

Question 7

A polynomial function $$f(x)$$ has zeros at $$x=-2 ($$multiplicity 1), $$x=1 ($$multiplicity 2), and $$x=3 ($$multiplicity 1). Which statement about the graph is correct?

Accepted Answer

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

Question 8

Which of the following is the minimum degree of a polynomial whose graph has 4 turning points?

Accepted Answer

$$5$$

Question 9

If the leading coefficient of a polynomial of even degree is positive, what is the end behavior of the graph?

Accepted Answer

Both ends go up as $$x 	o \infty$$ and $$x 	o -\infty.$$

Question 10

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

Accepted Answer

$$x=0 ($$multiplicity 2), $$x=3 ($$multiplicity 1)

Question 11

A polynomial function $$f(x)$$ has the following end behavior: as $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty. $$Which of the following could be the degree and leading coefficient of $$f(x)$$?

Accepted Answer

Degree is odd, leading coefficient is negative.

Question 12

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

Accepted Answer

The graph has sharp corners.

Question 13

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 at $$x=2.$$

Question 14

Which of the following is a possible polynomial function for a graph that touches the x-axis at $$x=0$$ and crosses at $$x=2$$?

Accepted Answer

$$f(x) = x^2$(x-2)$$

Question 15

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

Accepted Answer

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

Question 16

If $$f(x) = (x-1)^2$(x+2)^3$, how many x-intercepts does the graph have?

Accepted Answer

2

Question 17

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

Accepted Answer

The graph is symmetric about the y-axis and both ends go up.

Polynomial Functions and Their Graphs: Study Notes for Precalculus

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