Graphing Rational Functions and Asymptotes

The horizontal asymptote equals zero when:

• the degree of the numerator and denominator are equal

• the degree of the numerator is less than the degree of the denominator

• the degree of the numerator is greater than the degree of the denominator

• the numerator equals zero

What is the vertical asymptote? 

• x = 2

• y = 2

• x = 1

• y = 1

What is/are the vertical asymptote(s)?

• x=-2

• x=2 and x=3

• x=-3

• x=3

What are the asymptotes?

• x=-1 y = -3

• x=1 y = -3

• x=-1 y =3

• x=1, y=3

Is there a hole or a vertical asymptote?

• A hole when x = 2

• A vertical asymptote at x = 2

• there is no hole or vertical asymptote

Match the graph to the correct rational equation below.

• f(x)=x²/(x²+x-12)

• f(x)=4x²/(x²-x-12)

• f(x)=(2x²-2)/2x²

• f(x)=x/(x²+x-12)

What are the x-intercepts?

• x= 2/3

• x= 4, x = -2

• x= -8, x = 1

• x= -4, x = 2

What are the asymptotes?

• x=1, x= 2, y =1, y= 2

• x= 2, x=-2, y = 1

• x=2 y =-1

• x=1 y =2, y =-2

What (if any) holes exist?

• x=2

• x=2 and x=3

• x=-3

• x=3

What is the horizontal asymptote?

• y = -4

• y = 1

• x = 1

• y = -6