IXL - Determine end behavior using graphs (Precalculus practice)

Use the graph of

(

)

to find the limit. The dashed line is an asymptote.

lim

→∞

(

)

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Learn with an example

question

Use the graph of

(

)

to find the limit. The dashed line is an asymptote.

lim

→

–

∞

(

)

key idea

The limit

lim

→∞

(

)

is what the values of

(

)

approach as

increases without

bound.

This limit may or may not exist.

The limit

lim

→

–

∞

(

)

is what the values of

(

)

approach as

decreases without

bound.

This limit may or may not exist.

The line

is a horizontal asymptote of the graph of

(

)

if and only if at least one of the limits

lim

→

–

∞

(

)

lim

→∞

(

)

solution

To find

lim

→

–

∞

(

)

look at what happens to the graph of

(

)

decreases without bound.

The graph of

(

)

approaches the horizontal asymptote

decreases without bound. So,

lim

→

–

∞

(

)

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HH.4Find limits at vertical asymptotes using graphs

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