Rational Function Discontinuity

Define discontinuity.

• Is a function that contains a hole, jump or break in its graph.

• Is a function that is not continuous.

• Is a function that has x-values that are restricted from the domain.

• Is a function's graph that contains holes or vertical asymptotes.

These are the factors left in the numerator after the rational function is simplified. They are the point(s) that cross the x-axis and have a y-value of 0.

• holes

• vertical asymptotes

• x-intercepts

• points

What is the x-intercept, vertical asymptote, hole, and domain?

Where is the removable discontinuity?

• x=2

• x=2 and x=3

• x=-3

• x=3

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 is the Vertical Asymptotes? 

• x= -5

• x= 5

• x= 6

• x= -6

What is the Vertical Asymptotes?

• x= -4

• x= -4,5

• x= -5,5

• x= 4

What is the horizontal asymptote of the function given?

• y = 2

• x = 1

• x = 2

• y = -1

What are the asymptotes?

• x = -3        y = 1  

• x = 3         y = 1

• x = -3        y = -1

• x = 3         y = -1

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.