Chapter 9 Rational Equations and

Functions9.2 Graphing Simple Rational Functions

What do you think our domain is?

What about our range?

What do you think our domain is?

What about our range?

There are two ways to write a rational function

There are two ways to write a rational function: Way One

Our asymptote at x = h is because it is outside of our domain, X DOES NOT EXIST THERE, so our graph cannot exist there.

Our asymptote at y = k is because it is outside of our domain, Y DOES NOT EXIST THERE, so our graph cannot exist there.

There are two ways to write a rational function: Way Two

Our vertical asymptote is where x cannot exist. So where cx+d (the denominator) is equal to zero. It is NOT in the domain.

Our horizontal asymptote is where y does not exist, meaning y = a/c is not in the range.

Graphing Rational FunctionsStep 1: find and draw the vertical and horizontal asymptotes

Step 2: create a table with two x values to the left of the vertical asymptote, and two x values to the right of the vertical asymptote

Step 3: complete the table for the y values and graph the four points

Step 4: draw a hyperbola through the points and avoid crossing any asymptotes

Homework

9.2 # 11,13,15,23,25,33,35,37,41