Math 131 Chapter 3 Problem Set

a. Use the Leading Coefficient Test to de termine the graph 's end behavior. b. Find the
x- intercepts and state whether the graph crosses the x-axis or touches the x-axis and
turns around at each intercept. c. Find the y-intercept by computing f(0). d. Determine
whether the graph has y-axis symmetry, origin symmetry, or neither. e. Graph the
function.

a. What is the graph's end behavior?

The graph of f(x) rises left and rises right.
The graph of f(x) rises left and falls right.
The graph of f(x) falls left and rises right .
The graph of f(x) falls left and falls right

b. What are the x-intercepts?

(Use a comma to separate answers as needed.)

Which zeros cross the x-axis?

(Use a comma to separate answers as needed. Type N if there is no solution .)

Which zeros touch the x-axis and turn around?

(Use a comma to separate answers as needed. Type N if there is no solution.)

c. What is the y-intercept?

f(0)=

d. Determine the symmetry of the graph.

Even ; y-axis symmetry
Odd ; origin symmetry
Neither

e. Determine the graph of the function.

The bar graph shows the cumulative number of deaths from AIDS in the United States, from 1990 through each of the years 1996 to 2002. The data in the graph can be modeled by the fol lowing polynomials , in which f(x) and g(x) re present the cumulative number of AIDS deaths x years after 1990.

Use f(x) to find the cumulative number of AIDS deaths in 2000. Use g(x) to find the cumulative number of AIDS deaths in 2000. Which function is a better description for the actual number shown in the bar graph? Cannot be determined.

Use the seven step method described in the book to graph the following rational function .

1. Select the symmetry of the function.

The function is symmetric about the y-axis
The function is symmetric about the origin
The function has no symmetric about the y-axis or the origin

2. Type the y-intercept, if any:
(Round to two decimal places . Type N if there is no y-intercept.)

3. Type the x-intercept(s), if any:
(Use a comma to separate answers if needed. Type N if there are no x-intercepts.)

4. What are the x- coordinates of the vertical asymptote(s)?
(Use a comma to separate answers if needed. Type N if there are no vertical
asymptotes.)

5. What is the y-coordinate of the horizontal asymptote?
(Type N if there are no vertical asymptotes.)

6. Type the y-coordinate for each of the following points:

(Round each answer to two decimal places.)

7. Using the information determined above, select the graph of the rational function.

10.

a. Find the slant asymptote of the graph of the rational function and b. Follow the
seven-step strategy and use the slant asymptote to graph the rational function.

a. Find the slant asymptote of the graph of f.

y=

(Type N if there is no slant asymptote.)

b. Follow the seven-step strategy and use the slant asymptote to graph f.

Determine the symmetry of the graph of f.

The graph has y-axis symmetry .
The graph has origin symmetry .
The graph has both y-axis and origin symmetry
The graph has neither y-axis and origin symmetry

Find the y-intercept(s).

The y-intercept is .
(Type an integer or a simplified fraction . Use a comma to separate answers as needed.
Type N if there is no y-intercept.)

Find the x-intercept(s).

The x-intercept is .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.
Type N if there is no x-intercept.)

Find the vertical asymptote(s).

x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.
Type N if there is no vertical asymptote.)

Find the horizontal asymptote(s).

y=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.
Type N if there is no horizontal asymptote.)

Plot points between and beyond each x-intercept and vertical asymptote, then use the
information above to graph the rational function. Choose the correct graph below.

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