Removable Rational Function

Where is the removable discontinuity?

• x=2

• x=2 and x=3

• x=-3

• x=3

What are the x-intercepts?

• x= 2/3

• x= 4, x = -2

• x= -8, x = 1

• x= -4, x = 2

What is the horizontal asymptote of the function given?

• y = 2

• x = 1

• x = 2

• 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.

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• The function is discontinuous at x={-5, -3}

• There is a hole at x=3

• There is a hole at x= -2

• The horizontal asymptote is at y=0

• The domain is {x|x≠2,3}

What are the asymptotes?

• x=-1 y = -3

• x=1 y = -3

• x=-1 y =3

• x=1, y=3

Choose the type of Discontinuity on the given graph

• Jump

• Infinite

• Removable

• Rational

Examine the given function below and classify it accordingly.

• Discontinuous at x=3; Jump                 

• Discontinuous at x=3; Removable        

• Discontinuous at x=3; Infinite

• Continuous

Lily, Evelyn, and Scarlett are studying rational functions in their math class. They come across a problem that asks, 'What is the difference between a removable and non-removable discontinuity in a rational function?' How would you explain this to them?

• A removable discontinuity can be filled by removing a value from the function at that point, like erasing a pencil mark on a graph, while a non-removable discontinuity cannot be filled by removing a value from the function at that point, like a permanent marker line on a graph.

• A removable discontinuity occurs when the function is undefined at a certain point, like a hole in a road, while a non-removable discontinuity occurs when the function is defined at a certain point, like a bridge over a river.

• A removable discontinuity can be fixed by changing the function's equation, like fixing a broken toy with a new part, while a non-removable discontinuity cannot be fixed by changing the function's equation, like a shattered vase that can't be put back together.

• A removable discontinuity can be filled by assigning a value to the function at that point, like filling a hole in a wall with plaster, while a non-removable discontinuity cannot be filled by assigning a value to the function at that point, like a window in a wall that can't be filled with plaster.

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