1. Lesson 2-7: Graphing Rational Functions
Advanced Math Topics

2. Definitions
Continuity: a graph that is able to be traced without picking up the pencil
Asymptote: a line that the graph of the function approaches, but never touches (graphed as a dotted line)
Point discontinuity: a hole in the graph

3. Vertical Asymptote
To find a vertical asymptote: set the denominator factor(s) equal to zero and solve

4. Horizontal Asymptote To Find A Horizontal asymptote :look at the
degrees of the numerator
and denominator
*If the degree of
the denominator is
greater than the degree
of the numerator,
then the horizontal
asymptote is y=0
equal to the degree
of the numerator
asymptote is found by
dividing the coefficients
of the leading terms.
y=1, is the
horizontal asymptote
because the
coefficients of the
leading terms = =1

5. Point Discontinuity
Point discontinuity happens when you factor the numerator and denominator and the denominator factor is canceled.
The value of x that makes the denominator zero is the point of discontinuity.

6. Evaluate Rational Functions just like you would any other function
Evaluate Rational Functions just like you would any other function. Finding f(4) simply means plug 4 in for x.
When you are looking for x and you know f(x) = some # then you replace the f(x) in function notation with the # you are given and solve for x

7. Find f(-4) and then find x when f(x) = 2

8. Word Problems
Roy took two tests and his average is 63. If he scores 100 on the rest of his tests, how many more tests does Roy need to take to raise his average to 85?

9. Steps to Graph a Rational Function
1. Factor and simplify if you can
2. Look for the vertical asymptote and horizontal asymptote
3. Draw asymptotes as dotted lines on your graph
5. Find 3 x values greater than the vertical asymptote and 3 less than the vertical asymptote
( If there is no vertical asymptote you must make a t-chart and find at least 5 points to sketch the graph)
6. graph the points and stretch the curve toward the asymptotes.

10. Graphing Rational Functions

11. Graphing Rational Functions

12. Graphing Rational Functions

13. Graphing Rational Functions