Let
f
(
x
)
=
{
2
x
+
10
if
x
<
2
26
−
5
x
if
x
>
2
−
2
if
x
=
2
\displaystyle {f{{\left({x}\right)}}}={\left\lbrace\begin{array}{ccc} {2}{x}+{10}&\text{if}&{x}<{2}\\{26}-{5}{x}&\text{if}&{x}>{2}\\-{2}&\text{if}&{x}={2}\end{array}\right.}
f
(
x
)
=
⎩
⎨
⎧
2
x
+
10
26
−
5
x
−
2
if
if
if
x
<
2
x
>
2
x
=
2
Determine whether f(x) is continuous at
x
=
2
\displaystyle {x}={2}
x
=
2
. If f(x) is not continuous, identify why.
Not continuous:
f
(
2
)
\displaystyle {f{{\left({2}\right)}}}
f
(
2
)
is undefined.
Not continuous:
lim
x
→
2
f
(
x
)
≠
f
(
a
)
\displaystyle \lim_{{{x}\to{2}}}\ \ {f{{\left({x}\right)}}}\ne{f{{\left({a}\right)}}}
x
→
2
lim
f
(
x
)
=
f
(
a
)
.
Not continuous:
lim
x
→
2
f
(
x
)
\displaystyle \lim_{{{x}\to{2}}}\ \ {f{{\left({x}\right)}}}
x
→
2
lim
f
(
x
)
does not exist.
The function is continuous at
x
=
2
\displaystyle {x}={2}
x
=
2
.
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