4.1 4.2 Rational Functions

What are the vertical asymptotes of the function f(x)=(x²-9)/(x²+6x+9)

• x=3

• x=-3

• x=3,-3

• no vertical asymptote

What is the horizontal asymptote?

• y = -4
• y = 1
• x = 1
• y = -6

Find the horizontal asymptote.

• y = -2
• none
• y = 0
• y = 1/2

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on
• there is something left in the denominator
• the value of f(0)
• a factor in the denominator cancels with a factor in the numerator

Which of the following represent(s) the domain of the function shown?

What is the DOMAIN?

• All Real Numbers

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)

Which graph matches the function?

• A

• B

• C

• D

Which graph matches the function?

• A

• B

• C

• D

What is the interval of increasing/decreasing?

• Increasing : (-infinity, 1) Decreasing (1, infinity)

• Decreasing : (-infinity, 1) (1, infinity)

• Increasing (-infinity, -4) Decreasing (-4, infinity)

• Decreasing (-infinity, -4) (-4, infinity)