IXL - Find and analyze points of discontinuity using graphs (Precalculus practice)

The graph shows

(

)

List the

-values

where

(

)

has a discontinuity.

Write your answer as a single value or a list of values separated by commas.

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question

The graph shows

(

)

List the

-values

where

(

)

has a discontinuity.

Write your answer as a single value or a list of values separated by commas.

key idea

A function

(

)

has a discontinuity at an

-value

(

)

is not continuous at

solution

To find where

(

)

has a discontinuity, look for breaks in the graph. To confirm these breaks are discontinuities, look at the one-sided limits of

(

)

at these

-values.

Use the graph to find the left-hand and right-hand limits of

(

)

–

From the graph,

lim

→

–

(

)

–

and

lim

→

–

(

)

–

Since the limits are different,

lim

→

–

(

)

does not exist. So,

(

)

has a discontinuity at

–

The

-value

where

(

)

has a discontinuity is

–

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II.2Determine continuity using graphs

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