Lesson 2-7: Graphing Rational Functions

Advanced Math Topics

Mrs. Mongold

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 (this line is graphed as a dotted line)

• Point discontinuity: a hole in the graph

Vertical Asymptote

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.

Point Discontinuity

Steps to Graph a Rational Function

• 1. Factor and simplify if you can• 2. Look for the vertical asymptote• 3. Look for the horizontal asymptote• 4. Draw asymptotes as dotted lines on your graph• 5. Find 2 x values so that one is greater than the vertical

asymptote and one is less than the vertical asymptote ( If there is no vertical asymptote you must make an x-y chart and find at least 5 points to sketch the graph)

• 6. Plot the two points and sketch the graph by stretching toward the asymptotes.

Graphing Rational Functions

xxf

1)(

•

Graphing Rational Functions

1

1)(

x

xf

•

Graphing Rational Functions

1

32)(

2

x

xxxf

Graphing Rational Functions

1

5)(

2 x

xf

Homework

• Pg 124/ 12-18 Even

Day #2

• 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) = 3

1

32)(

2

x

xxxf

Find g(t)=-3

5

1)(

t

ttg

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?

• Arlene realized while she was making plans for her children’s education that she was seven times as old as her youngest child, Mark, who is 5 years old. In how many years will Arlene be twice as old as Mark?

Homework

• Pg 124/ 2-9