Q: Which of the following describes the end behavior of $$f(x) = -x^7$ + 1$$?

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

Question 1

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$g(x) = x$$^{1/3}$$

Question 2

What is the degree of the polynomial $$f(x) = 3x^5$ - 2x^3$ + x - 7$$?

Accepted Answer

$$5$$

Question 3

Which property is true for the graph of any polynomial function?

Accepted Answer

It is smooth and continuous.

Question 4

Given $$f(x) = x^6$, which of the following statements is correct?

Accepted Answer

The graph is symmetric about the y-axis.

Question 5

If $$f(x) = (x-2)^3$(x+1)^2$$, what is the multiplicity of the zero at $$x=2$?

Accepted Answer

$$3$$

Question 6

For the polynomial $$f(x) = (x+1)(x-2)(x-3)$$, which of the following is true about its x-intercepts?

Accepted Answer

The graph crosses the x-axis at $$x=-1$$, $$x=2$$, and $$x=3.$$

Question 7

Which of the following describes the end behavior of $$f(x) = -x^7$ + 1$$?

Accepted Answer

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

Question 8

A polynomial function $$f(x) of $$degree $$n$$ can have at most how many turning points?

Accepted Answer

$$n-1$$

Question 9

If $$f(x) = (x-3)^2$(x+4)$$, what is the behavior of the graph at $$x=3$$?

Accepted Answer

The graph touches the x-axis.

Question 10

Which of the following is a power function of degree 4?

Accepted Answer

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

Question 11

Given $$f(x) = (x+1)(x-1)(x-2)^2$, what is the least possible degree of f(x$$)$$?

Accepted Answer

$$4$$

Question 12

If a polynomial function $$f(x)$$ has a real zero $$r of $$even multiplicity, what happens at $$x=r$$?

Accepted Answer

The graph touches the x-axis.

Question 13

Which of the following is NOT a property of the graph of $$f(x) = x^n$$ for $$n a $$positive odd integer?

Accepted Answer

The graph is symmetric about the y-axis.

Question 14

A real-world scenario: The height $$h (in $$meters) of a projectile launched upward can be modeled by $$h(t) = -4.9t^2$ + 20t + 2. $$What type of function is this?

Accepted Answer

Quadratic function

Question 15

If $$f(x) = (x+1)(x-2)(x-3)$$, what is the y-intercept of $$f(x)$$?

Accepted Answer

$$-6$$

Question 16

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

Accepted Answer

A graph with a gap at $$x=1.$$

Question 17

If $$f(x) = (x-1)^2$(x+2)$$, what is the degree of $$f(x)$$?

Accepted Answer

$$3$$

Question 18

For $$f(x) = x^4$, what is the end behavior as x$$ 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 19

If $$f(x) = (x-2)^2$(x+3)$$, which x-intercept does the graph cross?

Accepted Answer

$$x=-3$$

Question 20

A polynomial function $$f(x)$$ has 4 turning points. What is the minimum possible degree of $$f(x)$$?

Accepted Answer

$$5$$

Finding a Polynomial Function from Its Real Zeros

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