Question

Determine which of the following functions are continuous. Select all that apply. \[ \begin{array}{l} f(x)=\frac{e^{x}+7}{\left|x^{3}+1\right|} \\ f(x)=\left\{\begin{array}{ll} \ln \left(x^{2}+1\right)+7, & \text { if } x<0 \\ 4 x+2, & \text { if } x \geq 0 \end{array}\right. \\ f(x)=\left\{\begin{array}{ll} 3 \sin x+\pi, & \text { if } x<\frac{\pi}{2} \\ \frac{4}{\pi} x^{2}+3, & \text { if } x \geq \frac{\pi}{2} \end{array}\right. \\ 3 x^{3}+5 x-1 \\ x^{2}+10 \begin{array}{ll} 10 & \text { if } x<4 \end{array} \\ f(x)=\left\{\begin{array}{ll} x^{2}-16, & \text { if } x \geq 4 \\ \sqrt{x-4}, \end{array}\right. \end{array} \]

          Determine which of the following functions are continuous. Select all that apply.
\[
\begin{array}{l}
f(x)=\frac{e^{x}+7}{\left|x^{3}+1\right|} \\
f(x)=\left\{\begin{array}{ll}
\ln \left(x^{2}+1\right)+7, & \text { if } x<0 \\
4 x+2, & \text { if } x \geq 0
\end{array}\right. \\
f(x)=\left\{\begin{array}{ll}
3 \sin x+\pi, & \text { if } x<\frac{\pi}{2} \\
\frac{4}{\pi} x^{2}+3, & \text { if } x \geq \frac{\pi}{2}
\end{array}\right. \\
3 x^{3}+5 x-1 \\
x^{2}+10 \begin{array}{ll}
10 & \text { if } x<4
\end{array} \\
f(x)=\left\{\begin{array}{ll}
x^{2}-16, & \text { if } x \geq 4 \\
\sqrt{x-4},
\end{array}\right.
\end{array}
\]

$Determine which of the following functions are continuous. Select all that apply. f(x)=(e^x+7)/(|x^3+1|) f(x)={ ln(x^2+1)+7, if x<0 4 x+2, if x ≥ 0 . f(x)={ 3 sin x+π, if x<(π)/(2) (4)/(π) x^2+3, if x ≥(π)/(2) . 3 x^3+5 x-1 x^2+10 10 if x<4 f(x)={ x^2-16, if x ≥ 4 √(x-4), .$

Added by Mohamed A.

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