definitions of the day (dods) 11.2 – graphing rational functions rational function asymptote

Definitions of the Day (DODs)

11.2 – Graphing Rational Functions

• Rational Function

• Asymptote

Definition: Rational Function:A function that can be written in the form

Examples:

polynomialpolynomial

f x

14

f xx

2

2y

x

2 3 22

x xg x

x

Definition: A line is an asymptote of a graph if the graph of the function gets closer and closer to the line, but does not cross it.

Example:The red lines are asymptotes.

One line is a vertical asymptote (x = 0).

The other line is a horizontal asymptote (y = 0).

Notice that the graph approaches the asymptotes, but does not cross them.

Finding Vertical Asymptotes

Evaluate each rational function for x = 3.

14

f xx

2

2y

x

2 3 22

x xg x

x

Find the vertical asymptote for each rational function.

To find vertical asymptotes, we will set the denominator equal to zero and solve for x.

14

f xx

2

2y

x

2 3 22

x xg x

x

Steps to graphing a rational function:

1. Find the vertical asymptote. The vertical asymptote is where the denominator equals zero.

2. Make a table of values around the asymptote.

3. Draw the graph (remember to show the asymptote by using a dashed line).

Graphing a rational function

Graph the function 4

3y

x

Graphing a rational function

Graph the function 3

2yx

Your Turn!!Evaluate the rational function for x = -2

61)

1f x

x

Graph the following function

22) y

2x

Sentence Frames

1. A rational function is a __________ over another ___________.

2. To find a vertical asymptote, I need to _________________________________________.