Vertical Asymptotes
Holes of Rational Functions
Horizontal Asymptotes
Solving Rational Equations
100

What is the difference between a hole in a graph and a vertical asymptote?

Vertical asymptote is a restriction on the denominator that cannot be cancelled out

100

Find the hole of the rational function below. 

((x-1)(x-4))/((x-4)(x+2))



(-4, 1/2)

100

The equation of the horizontal asymptote of y = 3/x


y = 0

100

x=12

200

The equation of a rational functions with two vertical asymptotes at x=3 and x=-5

Answers Vary

(x+5) and (x-3) in denominator

200

Find the hole of:

(3,1/2)

200

The equation of the horizontal asymptote of this function


What is y=2
200

x= -1/2 and 1

300
The equation of a rational function with a vertical asymptote at x = 2

Answers Vary


Ex)

(x-4)/(x-2)

300

Find the hole of:

(-2,-2)

300

The equation for the horizontal asymptote of the following graph


y = 1

300

x= 4


(-2 is extraneous) 

400

Write a rational function with a vertical asymptote at x=3 

Answers vary 

Ex) 

(2(x+1))/(x-3)

400

Graph the function below. Label all asymptotes, intercepts, and holes.

400

The horizontal asymptote of

(x-2)/(3x+4)

y = 1/3

400

No solution!

500

Write a rational function that has a hole when x=-1 and a vertical asymptote at x=3

y= ((x+1)(x-2))/((x+1)(x-3)

500

How is a hole created and how do I find it?

A hole is created when a factor is canceled out of the numerator and denominator of a rational function. This creates a "hole" in our graph at an (x,y) point.

500

The horizontal asymptote of  (x-2)/(x-3)

y = 1

500

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