Lesson 18

Graphs of Rational Functions (Part 2)

• Let’s learn about horizontal asymptotes.

Problem 1

Rewrite the rational function $$g(x) = \frac{x-4}{x}$$ in the form $$g(x) = c + \frac{r}{x}$$, where $$c$$ and $$r$$ are constants.

Problem 2

The average cost (in dollars) per mile for riding $$x$$ miles in a cab is $$c(x)=\frac{2.5+2x}{x}$$. As $$x$$ gets larger and larger, what does the end behavior of the function tell you about the situation?

Problem 3

The graphs of two rational functions $$f$$ and $$g$$ are shown. One of them is given by the expression $$\frac{2-3x}{x}$$. Which graph is it? Explain how you know.

Problem 4

Which polynomial function’s graph is shown here?

A:

$$f(x)=(x+1)(x+2)(x+5)$$

B:

$$f(x)=(x+1)(x-2)(x-5)$$

C:

$$f(x)=(x-1)(x+2)(x+5)$$

D:

$$f(x)=(x-1)(x-2)(x-5)$$

(From Unit 2, Lesson 7.)

Problem 5

State the degree and end behavior of $$f(x)=5x^3-2x^4-6x^2-3x+7$$. Explain or show your reasoning.

(From Unit 2, Lesson 9.)

Problem 6

The graphs of two rational functions $$f$$ and $$g$$ are shown. Which function must be given by the expression of $$\frac{10}{x-3}$$? Explain how you know.

(From Unit 2, Lesson 17.)