Lesson 2-7: Graphing Rational Functions Advanced Math Topics

Lesson 2-7: Graphing Rational Functions

Advanced Math Topics

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

Vertical Asymptote

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

Horizontal Asymptote

y=1, is the horizontal asymptote

because the coefficients of the

leading terms = =1

To Find A Horizontalasymptote :look at the

degrees of the numeratorand denominator

*If the degree of the denominator is

greater than the degree of the numerator,

then the horizontal asymptote is y=0

*If the degree ofthe denominator isequal to the degree

of the numeratorthen the horizontal

asymptote is found by dividing the coefficients

of the leading terms.

1

1

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.

• 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

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

2

8)(

2

x

xxxf

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?

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.

Graphing Rational Functions

xxf

1)(

•

Graphing Rational Functions

1

1)(

x

xf

•

Graphing Rational Functions

1

34)(

2

x

xxxf

Graphing Rational Functions

1

5)(

2 x

xf