Analyzing Rational Functions and Their Derivatives

What is the X-Intercept?

• x= 0
• x= 4
• x= 5
• x= -5

What are the x-intercepts?

• x= 2/3
• x= 4, x = -2
• x= -8, x = 1
• x= -4, x = 2

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 horizontal asymptote to this function?

• y=4
• y=0
• y=-2
• y=1

What (if any) holes exist?

• x=2

• x=2 and x=3

• x=-3

• x=3

What is/are the vertical asymptote(s)?

• x=-2
• x=2 and x=3
• x=-3
• x=3

What is the horizontal asymptote?

• y = -4
• y = 1
• x = 1
• y = -6

Factor and cancel out in order to simplify.

• 1/(n-7)

• n-7

• (n-6)/(n-7)

• n-6

Simplify the rational function

• 1/(x + 5)

• 1/(x - 5)

• (x - 5)(x + 5)

• (x - 5)/[(x - 5)(x + 5)]

Simplify (look for common factors that you can factor out and cancel out)

• A.4x³/(x+2)

• B.4x³/(x+10)

• C.2x³/(5x+1)

• D. 2x³/(x+5)