Q: Given the polynomial function $$f(x) = 2x^4$ - 6x^3$ + 6x - 2$$, what is the end behavior of the graph as $$x \to \infty$$ and $$x \to -\infty$$?

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

Question 1

Given the polynomial function $$f(x) = 2x^4$ - 6x^3$ + 6x - 2$$, what is the end behavior of the graph as $$x 	o \infty$$ and $$x 	o -\infty$$?

Accepted Answer

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

Question 2

For the polynomial $$f(x) = 3x^2$ + 12x + 12$$, what is the $$y-$$intercept?

Accepted Answer

$$y = 12$$

Question 3

Which of the following best describes the domain of any polynomial function?

Accepted Answer

$$(-\infty, \infty)$$

Question 4

Given $$f(x) = (x-3)^2$(x+1)$$, what is the multiplicity of the zero at $$x = 3$$ and how does the graph behave at this point?

Accepted Answer

Multiplicity 2; the graph touches and turns at the $$x-$$axis

Question 5

A chemical reaction rate is modeled by $$f(x) = x^3$ - 2x^2$ + x. $$What are the $$x-$$intercepts of the function?

Accepted Answer

$$x = 0, 1, 0$$

Question 6

For $$f(x) = x^3$ - 4x$$, which intervals should be used to analyze the graph between the $$x-$$intercepts?

Accepted Answer

$$(-\infty, 0), (0, \infty)$$

Question 7

A medical dosage model is given by $$f(x) = x^2$ - 6x + 8. $$What is the range of this function?

Accepted Answer

$$[4, \infty)$$

Question 8

Which of the following is NOT a step in graphing a polynomial function according to the study materials?

Accepted Answer

Calculate the derivative at each $$x-$$intercept

Question 9

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the $$y-$$intercept and how do you find it?

Accepted Answer

$$y = 1$$, by evaluating $$f(0)$$

Question 10

A polynomial $$f(x)$$ has zeros at $$x = -2 ($$multiplicity 1), $$x = 1 ($$multiplicity 2), and $$x = 3 ($$multiplicity 1). Which zero does the graph touch but not cross?

Accepted Answer

$$x = 1$$

Question 11

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

Accepted Answer

$$y = 0$$

Question 12

Which of the following best describes the range of $$f(x) = x^3$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

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

Accepted Answer

Both ends rise

Question 14

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

Accepted Answer

Crosses the $$x-$$axis at $$x = 2$$

Question 15

Which of the following is a correct step for determining intervals of unknown behavior in a polynomial graph?

Accepted Answer

Break the graph at each $$x-$$intercept

Question 16

For $$f(x) = x^2$(x-1)$$, what is the multiplicity of the zero at $$x = 0$$?

Accepted Answer

2

Question 17

A real-world population model is given by $$f(x) = -x^2$ + 4x - 3. $$What is the maximum value of the function?

Accepted Answer

$$f(2) = 3$$

Question 18

Which of the following is true about the graph of $$f(x) = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis

Question 19

For $$f(x) = x^3$ - 2x^2$ + x$$, what is the degree of the polynomial and what does it tell you about the number of turning points?

Accepted Answer

Degree 3; up to 2 turning points

Question 20

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

Accepted Answer

The graph touches and turns at $$x = -1$$

Graphing Polynomial Functions: Intervals, End Behavior, and Domain/Range

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