End Behavior Asymptote

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

• ∞

• -∞

• As the function approaches two, left and right of two do not match

• As the function approaches two, the graph oscillates.

• As the function approaches two, the graph increases or decreases without bound.

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

• ^-2/₉

• 0

• ∞

• -∞

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

As x → ∞ , y → ?

• -4

• -3

• ∞

• -∞

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

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 equation of the asymptote?

Mathematical Equivalence

ON