Roots Rational Functions

What are the x-intercepts?

• x= 2/3

• x= 4, x = -2

• x= -8, x = 1

• x= -4, x = 2

What is/are the x-intercepts of this graph?

• (-2,0) and (2,0)

• (-2,0)

• (3,0)

• (2,0) and (3,0

FIND THE ZEROS.

• X=7

• X = -3

• X = 0

• X=3

• Vertical Asymptote. at x = -3 and x = 1

• Hole at (1, 0)

• Horizontal Asymptote at y = 2

• x-intercepts at (3,0) and (1, 0)

Find the x-intercept(s), if one exists.

• (1, 0)

• (-1, 0)

• (1, 0), (-1, 0)

• (0, 0), (1, 0)

When is there a hole in the graph?

• If a factor in the denominator cancels, it'll cause a hole.

• If a factor in the denominator doesn't cancel.

• If the numerator is a constant.

• If the numerator is zero.

What (if any) holes exist? What are the zero/s of the function? HINT: To get started, factor both the numerator and denominator of the function.

• Hole   x=2     Zero x = -2

• Holes x=2 and x=3  Zeros None

• Hole  x=-3   Zeros x=2 and x=-2

• Hole x=2   Zeros x=2 and x=-2

Choose the best equation for the graph.

• 
• 
• 
• 

What are the coordinates of the hole, if one exists.

• (-1, -2)

• (-1, ½)

• (-1, -½)

• there isn't one

What are the asymptotes?

• x = -2 and y = -1

• x = -2 and y = 1

• x = 2 and y = 1

• x = 2 and y = -1