Let
f
(
x
)
=
{
4.7
x
+
23.8
if
x
<
−
4
x
+
29
if
x
>
−
4
−
2
if
x
=
−
4
\displaystyle {f{{\left({x}\right)}}}={\left\lbrace\begin{array}{ccc} {4.7}{x}+{23.8}&\text{if}&{x}<-{4}\\\sqrt{{{x}+{29}}}&\text{if}&{x}>-{4}\\-{2}&\text{if}&{x}=-{4}\end{array}\right.}
f
(
x
)
=
⎩
⎨
⎧
4.7
x
+
23.8
x
+
29
−
2
if
if
if
x
<
−
4
x
>
−
4
x
=
−
4
Determine which one of the following rules for continuity is violated at
x
=
−
4
\displaystyle {x}=-{4}
x
=
−
4
.
lim
x
→
a
f
(
x
)
\displaystyle \lim_{{{x}\to{a}}}\ \ {f{{\left({x}\right)}}}
x
→
a
lim
f
(
x
)
exists.
f
(
a
)
\displaystyle {f{{\left({a}\right)}}}
f
(
a
)
is defined.
lim
x
→
a
f
(
x
)
=
f
(
a
)
\displaystyle \lim_{{{x}\to{a}}}\ \ {f{{\left({x}\right)}}}={f{{\left({a}\right)}}}
x
→
a
lim
f
(
x
)
=
f
(
a
)
.
None of the above; the function is continuous at
x
=
−
4
\displaystyle {x}=-{4}
x
=
−
4
.
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