Rewrite the function as a piecewise function.
-$f(x)=|x+2|+7$
A) $f(x)=\left\{\begin{array}{l}-x+5 \text { if } x

Question

Rewrite the function as a piecewise function.
-$f(x)=|x+2|+7$
A) $f(x)=\left\{\begin{array}{l}-x+5 \text { if } x<2 \ x-9 \text { if } x \geq 2\end{array}\right.$

B) $f(x)=\left\{\begin{array}{r}-x+5 \text { if } x<-2 \ x+9 \text { if } x \geq-2\end{array}\right.$

C) $f(x)=\left\{\begin{array}{l}x+5 \text { if } x<2 \ -x+9 \text { if } x \geq 2\end{array}\right.$

D) $f(x)=\left\{\begin{array}{r}x-5 \text { if } x<-2 \ -x+9 \text { if } x \geq-2\end{array}\right.$

Quizplus · Accepted Answer

The correct piecewise function for $f(x)=|x+2|+7$ splits at $x=-2$, where the expression inside the absolute value changes sign. For $x<-2$, $|x+2|=-(x+2)$, so the function is $-x-2+7=-x+5$. For $x\geq-2$, $|x+2|=x+2$, so the function is $x+2+7=x+9$.

Rewrite the Function as a Piecewise Function f(x)=∣x+2∣+7f(x)=|x+2|+7f(x)=∣x+2∣+7 A) f(x)={−x+5 if x<2x−9 if x≥2f(x)=\left\{\begin{array}{l}-x+5 \text { if } x<2 \\ x-9 \text { if } x \geq 2\end{array}\right.f(x)={−x+5 if x<2x−9 if x≥2​

Rewrite the Function as a Piecewise Function $f(x)=|x+2|+7$ A) $f(x)=\left\{\begin{array}{l}-x+5 \text { if } x<2 \\ x-9 \text { if } x \geq 2\end{array}\right.$