Rational Function Asymptote

Fill in the blank: An ____________ is a line that a graph approaches.

Can you have more than one vertical asymptotes?

• Yes

• No

How many slant (oblique) asymptotes can you have?

• 3

• none

• 1

• 2

• 
• 
• 

How do you find a slant asymptote?

• by using long division

• by setting the denominator = 0 and solve for x

• by plugging 0 in for x's on the numerator

Which type of asymptotes can a graph pass through?

• Slant asymptote

• Vertical asymptotes

• Horizontal asymptote

• None

Find the vertical asymptote.
g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)} 

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• To finish finding the coordinates of a hole, place the x value in the reduced equation

The horizontal asymptote equals zero when:

• y=0

• the degree of the numerator is less than the degree of the denominator

• divide the coefficients

• the degree of the numerator is less by one or more of the denominator

• None

• the degree of the numerator is exactly one degree more than the demoninator

• y=0

• the degree of the numerator is greater than the degree of the denominator

• Slant asymptote

• the degree of the numerator and denominator are equal

Does this rational have a horizontal asymptote? If so what is it?

• No

• Yes, y=0

• yes, y=3

• yes, y=1/3

• No, but is has a slant asymptote