Q: A chemical reaction's rate can be modeled by $$f(x) = 2x^3$ - 5x^2$ + 3x - 1. $$According to the Leading Coefficient Test, what is the end behavior of this function?

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

Question 1

Which of the following is NOT a characteristic of the graph of a polynomial function of degree 3 or higher?

Accepted Answer

The graph can have sharp corners.

Question 2

Given the polynomial function $$f(x) = -2x^5$ + 3x^3$ - x + 7$$, what is the end behavior of its graph?

Accepted Answer

Rises to the left and falls to the right.

Question 3

Which of the following statements about the zeros of a polynomial function is TRUE?

Accepted Answer

The zeros of a polynomial function correspond to the $$x-$$intercepts of its graph.

Question 4

Consider the polynomial $$f(x) = x^4$ - 16. $$Which statement about its zeros is correct?

Accepted Answer

There are four real zeros, each with multiplicity 1.

Question 5

If a polynomial function $$f(x)$$ has a zero at $$x = 3$$ with multiplicity 2, what does the graph do at $$x = 3$$?

Accepted Answer

It touches the $$x-$$axis and turns around at $$x = 3.$$

Question 6

A chemical reaction's rate can be modeled by $$f(x) = 2x^3$ - 5x^2$ + 3x - 1. $$According to the Leading Coefficient Test, what is the end behavior of this function?

Accepted Answer

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

Question 7

Suppose $$f(x) = (x-1)^3$(x+2). $$Which of the following is TRUE about the zeros and their multiplicities?

Accepted Answer

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

Question 8

A polynomial $$f(x) of $$degree 6 is graphed. What is the maximum number of turning points the graph can have?

Accepted Answer

5

Question 9

Given $$f(x) = x^4$ - 4x^2$, which of the following describes the symmetry of the graph?

Accepted Answer

The graph is symmetric about the $$y-$$axis.

Question 10

A medical dosage model is given by $$f(x) = -x^4$ + 2x^2$ - 5. $$What is the end behavior of this function?

Accepted Answer

Falls to the left and right.

Question 11

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 6$$

Question 12

Suppose $$f(x) = x^2$(x-4). $$Which statement is TRUE about the behavior at $$x = 0$$?

Accepted Answer

The graph touches the $$x-$$axis and turns around at $$x = 0.$$

Question 13

A polynomial function $$f(x)$$ has $$f(-2) = -5$$ and $$f(1) = 3. $$What does the Intermediate Value Theorem guarantee?

Accepted Answer

There is at least one real zero between $$x = -2$$ and $$x = 1.$$

Question 14

Which of the following is the correct end behavior for $$f(x) = -x^3$ + 2x^2$ - x + 5$$?

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

A real-world population model is given by $$f(x) = 4x^3$ - 12x^2$ + 9x. $$How many $$x-$$intercepts does the graph have?

Accepted Answer

3

Question 17

Which of the following is the maximum number of $$x-$$intercepts a degree 5 polynomial can have?

Accepted Answer

5

Question 18

Given $$f(x) = x^4$ - 4x^2$, what are the zeros and their multiplicities?

Accepted Answer

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

Question 19

If $$f(x) = x^3$ - 4x$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, 0)$$

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