IXL - Determine continuity using graphs (Precalculus practice)

(

)

continuous at

–

yes

ref_doc_title.

Learn with an example

question

(

)

continuous at

yes

key idea

A function

(

)

is continuous at

if all three of the following statements are true:

g
(
x
)
is defined at
x
=
a
.
The limit
lim
x
→
a
g
(
x
)
exists.
The limit equals the value of the function:
lim
x
→
a
g
(
x
)
=
g
(
a
)

solution

To determine whether

(

)

is continuous at

check that all three of the following statements are true:

f
(
x
)
is defined at
x
=
0
.
The limit
lim
x
→0
f
(
x
)
exists.
The limit equals the value of the function.

Check whether

(

)

is defined at

Look at the graph.

The function

(

)

is defined at

Its value is

(

)

Check whether

lim

→0

(

)

exists.

Look at the graph.

From the graph,

lim

→0

(

)

exists and is equal to 1.

Check whether this limit is equal to

(

)

Both the limit and

(

)

equal 1.

So,

(

)

is continuous at

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Work it out

Not feeling ready yet? These can help:

HH.3Determine if a limit exists

II.1Identify graphs of continuous functions

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