End Behavior Asymptotes

Which of the following actions are appropriate for finding a limit at infinity? Look for multiple answers.

• If the function is polynomial, look at rules for end behavior.

• If the function has a HA, that will determine the limit at infinity.

• If the function has a slant asymptote, look at the end behavior of that line (the slant asymptote)

• Look at the function graphically to determine end behavior.

Find the limit. Hint: Where is the horizontal asymptote?

• ³/₇

• 0

• ∞

• -∞

Find the limit. Hint: Where is the horizontal asymptote?

• ^-2/₉

• 0

• ∞

• -∞

Which statement is true about slant asymptotes?

• Slant asymptotes can be a vertical or horizontal line graphically.

• Slant asymptotes are oblique (not purely vertical or horizontal) lines graphically.

• Slant asymptotes occur when the degree of the denominator is greater.

• Slant asymptotes occur when the degree of the numerator and denominator are equal.

Describe the end behavior for h\left(x\right)=-\log_3\left(x+1\right). Select ALL that apply.

As x → − ∞

• y → ∞

• y → − ∞

• y → 0

What is the end behavior of the graph?

• As x →∞, y→⁻∞ and as x →⁻∞, y→⁻∞

• As x →∞, y→∞ and as x→⁻∞, y→∞

• As is x →∞, y→∞ and as x→⁻∞, y→2

• As x →∞, y→2 and as x→⁻∞, y→∞

What is the end behavior of this function?

• 
• 
• 
•