Solving and Graphing Rational Equations

The x-intercepts of a rational function are :

• the real zeros of the denominator

• always zero

• the value of f(0)

• the real zeros of the numerator

What is the limit of the function as x approaches negative infinity?

• -2

• -3

• negative infinity

• positive infinity

Find the domain of the function.
x
__________
x²-4x-12

• (-∞,-2) u (-2,6) u (6, ∞)

• (-2,6)

• (-∞,2) u (2,6) u (6, ∞)

• (-∞,2) u (6 ,∞)

What is the slant asymptote of
f(x) = (4x²+3x-9)/(x-5)  ?

• y = 4x - 17

• none

• y = 4x + 23

• x = 5

Find the horizontal asymptote.
f(x) = (4x-16)/(x²-16)

• x = 4, x = -4

• y=1

• y=0

• none

Name any holes of the function.

• x=0

• none

• x=3

• x=-3

Solve and check for extraneous solutions.

• x=-1, x=-3 extraneous

• x=-1 extraneous, x=-2

• x=-1, x=-2 extraneous

• x=-1, x=2 extraneous

What is the horizontal asymptote?

• y=0

• y=1

• y=-1/9

• This graph does not have a horizontal asymptote.

Solve

• A

• B

• C

• D

Find the vertical asymptote(s).

• None

• x = 0

• x= 4

• x = -4, 4