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

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

Question 1

Which of the following best describes the function $$f(x) = 4x^5$ - 3x^2$ + 5x - 2$$?

Accepted Answer

It is a polynomial function of degree 5.

Question 2

Given the graph in Image 1, what is the maximum number of turning points for the polynomial shown?

Accepted Answer

$$3$$

Question 3

For the function $$f(x) = (x-1)^2$(x+3)(x+1)$$, which of the following statements is true about the behavior at $$x=1$$?

Accepted Answer

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

Question 4

Which of the following is the correct end behavior for the function $$f(x) = -2x^3$ + 4x^2$?

Accepted Answer

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

Question 5

Given the rational function $$R(x) = \frac{x+2}{x^2$-9}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 6

For the function $$R(x) = \frac{x^2$+4}{x-2}$$, which type of asymptote exists?

Accepted Answer

Oblique asymptote at $$y = x + 2$$

Question 7

Which of the following is NOT a possible rational zero of $$f(x) = 2x^3$ + 11x^2$ - 7x - 6$$ according to the Rational Zero Theorem?

Accepted Answer

$$2$$

Question 8

Given the graph in Image 5, what is the equation of the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 9

If $$h(x) = 3(x-7)(x+3)^2$, what is the multiplicity of the zero at x = -3$ and what does the graph do at this point?

Accepted Answer

Multiplicity 2, touches the x-axis

Question 10

Which of the following statements about the function $$g(x) = 2x^3$ - x^2$ + 2x - 3 is $$TRUE?

Accepted Answer

The function has at most 3 real zeros.

Question 11

Which of the following is the correct application of the Remainder Theorem for $$f(x) = x^4$ - 2x^3$ - 27$$ when divided by $$x+2$$?

Accepted Answer

The remainder is $$f(-2)$$

Question 12

Given the graph in Image 2, what is the y-intercept of the function?

Accepted Answer

$$y = 16$$

Question 13

For the rational function $$R(x) = \frac{x^2$ + 3x + 2}{(x+2)^2$}$$, what is the domain?

Accepted Answer

$$x \mid x 
eq -2$$

Question 14

Which of the following best describes the end behavior of $$f(x) = x(x+2)(x+4)$$?

Accepted Answer

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

Question 15

Which of the following is NOT a property of polynomial functions?

Accepted Answer

The graph can have vertical asymptotes.

Question 16

Given $$f(x) = (x-1)^2$(x+3)(x+1)$$, what is the maximum number of turning points?

Accepted Answer

$$3$$

Question 17

If $$f(x) = x^4$ - 2x^3$ - 27$$ and $$(x-3) is a $$factor, what is the quotient when $$f(x) is $$divided by $$(x-3)$$?

Accepted Answer

$$x^3$$ + $$x^2 + 3x + 9$

Question 18

Which of the following is true about the graph in Image 4?

Accepted Answer

It has x-intercepts at $$x = -3, 1$$

Question 19

For the rational function $$R(x) = \frac{2x^2$ + 6x + 4}{x^2$ + 5x + 6}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Polynomial and Rational Functions: Key Concepts and Graphs

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