Question

Let \( f(x)=\left\{\begin{array}{lll}5 x+9 & \text { if } & x<3 \\ 39-5 x & \text { if } & x>3 \\ 23 & \text { if } & x=3\end{array}\right. \) Determine whether \( \mathrm{f}(\mathrm{x}) \) is continuous at \( x=3 \). If \( \mathrm{f}(\mathrm{x}) \) is not continuous, identify why. Not continuous: \( \lim _{x \rightarrow 3} f(x) \) does not exist. Not continuous: \( f(3) \) is undefined. Not continuous: \( \lim _{x \rightarrow 3} f(x) \neq f(3) \). The function is continuous at \( x=3 \).

          Let \( f(x)=\left\{\begin{array}{lll}5 x+9 & \text { if } & x<3 \\ 39-5 x & \text { if } & x>3 \\ 23 & \text { if } & x=3\end{array}\right. \)
Determine whether \( \mathrm{f}(\mathrm{x}) \) is continuous at \( x=3 \). If \( \mathrm{f}(\mathrm{x}) \) is not continuous, identify why.
Not continuous: \( \lim _{x \rightarrow 3} f(x) \) does not exist.
Not continuous: \( f(3) \) is undefined.
Not continuous: \( \lim _{x \rightarrow 3} f(x) \neq f(3) \).
The function is continuous at \( x=3 \).

Let f(x)={
5 x+9 if x<3
39-5 x if x>3
23 if x=3
.
Determine whether f(x) is continuous at x=3. If f(x) is not continuous, identify why.
Not continuous: limx → 3 f(x) does not exist.
Not continuous: f(3) is undefined.
Not continuous: limx → 3 f(x) ≠ f(3).
The function is continuous at x=3.

Added by Teodora B.

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