Graphing Rationals

• x = 8

• x = 1

• x = 1 and x = -5/2

• x = -8

• y = 0

• y = 1

• There is no horizontal asymptote.

Label the graph

b

c

d

e

a

Vertical Asymptote

Horizontal Asymptote

y-intercept

origin

x-axis

What is the dotted line on the graph that the line never touches?

• dotted line

• inequality

• asymptote

• bold line

What are the asymptotes?

• x = -3        y = 1  

• x = 3         y = 1

• x = -3        y = -1

• x = 3         y = -1

Where are the vertical asymptote(s) in the function?

• x=2, x=-2

• x=6

• x=0

• x=4, x=-4

How do we know if we have a Vertical Asymptote.

• From BOBO BOTN EATS DC

• It is created by a factor that does not get canceled out.

• We do synthetic division.

• It is created by a factor that gets canceled out.

We determine a hole in a graph by:

• Using the x value from the factor that didn't cancel out.

• Using BOBO BOTN EATS DC

• Taking the x value of the POD factor, that canceled, and plugging it into our simplified version of our rational function.

• We divide the coefficients.

This rational function is a:

• BOBO

• BOTN

• EATS DC

• Linear

This rational function is a

• BOBO

• BOTN

• EATS DC

• Linear