Lesson Check

Do y o u k n o w H OW?

1. What is the excluded value for y = —l-


2. What are the asymptotes of f{x) = y-—g + 3? Graph
   the function.


3. The function t = ^ + 0.5 models the total time f,
   in hours, it will take you to travel 240 mi at r mi/h,
   assuming you stop for a half-hour break along the
   way. Graph this function. What must your average
   speed be in order for your travel time to be about 4 h?

MATHEMATICAL

Do yo u UN DERSTAND? PRA CTICES

4. Vocabulary Find the excluded value and the
   vertical and horizontal asymptotes of the function
   x - 5 +1.


5. Reasoning Write an example of a rational function
   with a vertical asymptote at x = -2 and a horizontal
   asymptote at y = 4.


6. Er r o r A n al y si s Your friend says that the vertical
   asymptote of the graph of f{x) = jqrg + 2 is x = 5.
   Describe and correct your friend’s error.


7. Compare and Contrast How are an excluded value
   and a vertical asymptote of a rational function alike?
   How are they different?

MATHEMATICAL

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses PRA CTICES

Pr act i ce Identify the excluded value of each rational function.

3- fix) = x 9. y = x - 2 y = x + 2

Identify the vertical and horizontal asymptotes of each graph.

13. J

1

—\

(^1) Tii
°T ~
Se e Pr o b l e m 1.
-3
2x-6
Se e Pr o b l e m s 2 an d 3.

11. h{x) =

Identify the asymptotes of the graph of each function. Then graph the function.

15.y = ;

19- y —;

16. y -10X ,7-TW = ;4-5
    2


17. h{x) x+1+ 4


18. g(x) =


19. f{x) = x _ 3

x + 4

-1 -5

23. Nutrition For lunch, you bought two veggie pizzas for you and your friends to ^ Se e Pr o b l e m 4.
    divide evenly. Each pizza contains 960 Calories. In addition, each person eats a
    banana, which contains 100 Calories.
    a. Write and graph an equation that gives the number of Calories C consumed by
    each person as a function of the total number of people n.
    b. Approximately how many people must share the pizzas in order for each person
    to consume about 500 Calories?

710 Chapter 11 Rat i o n al Ex p r essi o n s an d Fu n ct i o n s