Given the function below, determine if the function is continuous at the point
x
=
−
4
\displaystyle {x}=-{4}
x
=
−
4
. If not, indicate why.
f
(
x
)
=
x
2
−
4
x
+
4
\displaystyle {f{{\left({x}\right)}}}=\frac{{{x}^{{2}}-{4}}}{{{x}+{4}}}
f
(
x
)
=
x
+
4
x
2
−
4
Continuous at
x
=
−
4
\displaystyle {x}=-{4}
x
=
−
4
Not continuous:
f
(
−
4
)
\displaystyle {f{{\left(-{4}\right)}}}
f
(
−
4
)
is not defined; this is a removable discontinuity
Not continuous:
f
(
−
4
)
\displaystyle {f{{\left(-{4}\right)}}}
f
(
−
4
)
is not defined; this is
not
a removable discontinuity
Not continuous:
lim
x
→
−
4
f
(
x
)
\displaystyle \lim_{{{x}\rightarrow-{4}}}{f{{\left({x}\right)}}}
x
→
−
4
lim
f
(
x
)
does not exist
Not continuous:
f
(
−
4
)
\displaystyle {f{{\left(-{4}\right)}}}
f
(
−
4
)
and limit exist, but are not equal
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