Rational Functions and Their Discontinuities and Intercepts

Find the vertical asymptote(s).

• x = 3 and x = -7

• x = 3

• x = -7

• x = -4

What are the x-intercepts?

• (2/3, 0)

• (4,0) and (-2,0)

• (-8,0) and (1,0)

• (-4,0) and (2,0)

Which function matches this graph?

Choose the correct graph that matches with the equation.

• A

• B

• C

• D

Write an equation for a rational function with an x-intercept of (–1, 0), a hole at x = 3, and a VA at   x = 4. 

• y= (x-1)(x+3) / (x+4)(x+3)

• y= (x-4)(x-3) / (x+1)(x-3)

• y= (x+1)(x-3) / (x-4)(x-3)

• y= (x+4)(x+3) / (x+1)(x+3)

Select all the following statements that are true.

• Vertical asymptote at x=1

• Vertical asymptote at x=0

• No vertical asymptote

• Hole at (-1, 0)

• Hole at (1, -1)

Where is the hole?

• x= 4

• x= -4

• x= 5

• x= -5

Where is there a hole on the graph of the function?

• x = 2

• x = -2

• There are no holes.

• x = 5

How many vertical asymptotes does the function have?

• None

• 1

• 2

• 3

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3