Steps to Graphing a Rational Function

AP Precalculus Unit 1.7? I know for a fact this is from Unit 1, this also works for Algebra II!

Step 1

Factor the expression!

Step 2

Vertical Asymptote - Set the denominator equal to zero and solve for X. For example, x-3 = 0! X=3

Step 3 - y=0

If degree of numerator < denominator

Step 3 - y=coef/coef

Do this if the degree of the numerator and denominator are the same

Step 3 - slant asymptote

If degree of numerator > denominator

Step 4 - find x int

Set the whole numerator to zero then solve the numerator.

Step 6 - find the y int

Make x=0

Step 7 - find the hole’s x value

Search for a factor that can be cancelled out such as (x+3)/(x+3) and set the x+3 equal to zero so you can find the x value of the hole

Step 7 find the hole’s y value

Insert what you found for the x value and plug it into the whole function, remember to substitute it for the (x+3) you already cancelled and subtract/add the remaining digits