Q: Which of the following best describes the end behavior of the polynomial function $$f(x) = -x^4$ + 7$$?

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

Q: Which of the following describes the leading coefficient test for $$f(x) = -2x^5$ + 3x^2$ - 1$$?

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 end behavior of the polynomial function $$f(x) = -x^4$ + 7$$?

Accepted Answer

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

Question 2

Given the rational function $$R(x) = \frac{(x-1)(x+2)}{(x-1)(x-4)}$$, which value(s) of $$x$$ correspond to a hole in the graph?

Accepted Answer

$$x = 1$$

Question 3

What is the domain of the rational function $$R(x) = \frac{x^2$ - 4}{x^2$ - 5x + 6}$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = 3$$

Question 4

A chemical reaction rate is modeled by $$R(t) = \frac{2t}{t^2$ + 1}. $$What is the horizontal asymptote of $$R(t)$$?

Accepted Answer

$$y = 0$$

Question 5

Which of the following is a vertical asymptote of $$f(x) = \frac{x+3}{x^2$ - 9}$$?

Accepted Answer

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

Question 6

Solve the inequality $$(x-2)(x+1)(x-5) \geq 0$$ and select the correct solution set.

Accepted Answer

$$x \leq -1 or$$ $$2 \leq x \leq 5$$

Question 7

A population model is given by $$P(x) = 3x^3$ - 2x^2$ + x - 5. $$What is the degree of this polynomial?

Accepted Answer

3

Question 8

Which statement is true about the Fundamental Theorem of Algebra?

Accepted Answer

Every polynomial equation of degree $$n$$ has at least one complex root.

Question 9

Find all real zeros of $$f(x) = 2x^3$ - 3x^2$ - 11x + 6.$$

Accepted Answer

$$x = -2, x = 3, x = 1$$

Question 10

A rational function $$R(x)$$ has a numerator degree less than its denominator degree. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 11

Which of the following is a possible rational zero of $$f(x) = 6x^3$ + 5x^2$ - 7x + 2$$ according to the Rational Root Theorem?

Accepted Answer

$$x = \frac{1}{2}$$

Question 12

If $$f(x) = x^2$ + 4 = 0$$, what are the solutions?

Accepted Answer

$$x = 2i, x = -2i$$

Question 13

A rational function $$R(x) = \frac{ax^2$ + bx + c}{dx^2$ + ex + f}$$ has equal degrees in numerator and denominator. What is the horizontal asymptote?

Accepted Answer

$$y = \frac{a}{d}$$

Question 14

Which of the following describes the leading coefficient test for $$f(x) = -2x^5$ + 3x^2$ - 1$$?

Accepted Answer

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

Question 15

A rational function $$R(x)$$ has a hole at $$x = 2$$ and a vertical asymptote at $$x = 5. $$Which could be its formula?

Accepted Answer

$$R(x) = \frac{(x-2)(x+1)}{(x-2)(x-5)}$$

Question 16

Which of the following is NOT a step in graphing a rational function?

Accepted Answer

Set all coefficients to zero

Question 17

If a polynomial $$f(x)$$ has real coefficients and a complex zero $$z = 3 + 2i$$, what must also be a zero?

Accepted Answer

$$z = 3 - 2i$$

Question 18

A rational function $$R(x) = \frac{x^2$ - 1}{x^2$ - 4} is $$used to model the concentration of a drug in the bloodstream. What is the domain of $$R(x)$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = -2$$

Question 19

Which of the following is a correct application of synthetic division to test if $$x = 1 is a $$root of $$f(x) = x^3$ - 2x^2$ + x - 2$$?

Accepted Answer

The remainder is 0, so $$x = 1 is a $$root.

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