The graph below is the function
f
(
x
)
=
sin
(
∣
(
x
−
4
)
(
x
−
5
)
∣
)
(
x
−
4
)
(
x
−
5
)
\displaystyle {f{{\left({x}\right)}}}=\frac{{\sin{{\left({\left|{\left({x}-{4}\right)}{\left({x}-{5}\right)}\right|}\right)}}}}{{{\left({x}-{4}\right)}{\left({x}-{5}\right)}}}
f
(
x
)
=
(
x
−
4
)
(
x
−
5
)
sin
(
∣
(
x
−
4
)
(
x
−
5
)
∣
)
Select all statements below with which you agree.
Note: You may be checking more than one box. No partial credit.
f
(
4
)
\displaystyle \ {f{{\left({4}\right)}}}
f
(
4
)
is defined.
lim
x
→
4
f
(
x
)
\displaystyle \lim_{{{x}\to{4}}}\ \ {f{{\left({x}\right)}}}
x
→
4
lim
f
(
x
)
exists.
lim
x
→
5
+
f
(
x
)
=
f
(
5
)
\displaystyle \lim_{{{x}\to{5}^{+}}}\ \ {f{{\left({x}\right)}}}={f{{\left({5}\right)}}}
x
→
5
+
lim
f
(
x
)
=
f
(
5
)
.
The function is continuous at x = 5.
The function is not continuous at x = 4.
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