IXL - Make a piecewise function continuous (Calculus practice)

Find the value of

that makes

(

)

continuous at

(

)

– 4 x 2 + 8	if x ≠ 2
k	if x = 2

ref_doc_title.

Learn with an example

question

Find the value of

that makes

(

)

continuous at

–

(

)

– x 2 + 8	if x ≠ – 3
k	if x = – 3

key idea

The function

(

)

is continuous at

if all three of the following statements are true:

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

solution

For

(

)

to be continuous at

–

both

(

–

)

and

lim

→

–

(

)

must exist and be equal to one another:

lim

→

–

(

)

(

–

)

The function

(

)

depends on an unknown constant

The value of

that makes this equation true will make

(

)

continuous at

–

Find

(

–

)

Find the expression that defines

(

)

when the value of

is exactly

–

(

)

– x 2 + 8	if x ≠ – 3
k	if x = – 3

So,

(

–

)

Find

lim

→

–

(

)

Find the expression that defines

(

)

for values of

near, but not equal to,

–

(

)

– x 2 + 8	if x ≠ – 3
k	if x = – 3

Use this expression to find the limit.

lim

→

–

(

)

lim

→

–

(

–

)

–

(

–

)

–

Solve for

lim

→

–

(

)

(

–

)

–

So,

–

will make

(

)

continuous at

–

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Work it out

Not feeling ready yet? These can help:

E.6Determine the continuity of a piecewise function at a point

E.3Determine one-sided continuity using graphs

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