Write an absolute value function that is equivalent to the given piecewise function.
-$f(x)=\left\{\begin{array}{c}-x-18 \text { if } x

Question

Write an absolute value function that is equivalent to the given piecewise function.
-$f(x)=\left\{\begin{array}{c}-x-18 \text { if } x<-4 \ x-10 \text { if } x \geq-4\end{array}\right.$

A) $f(x)=|x-4|-14$

B) $f(x)=|x-14|+4$

C) $f(x)=|x+4|-14$

D) $f(x)=|x+14|-4$

Quizplus · Accepted Answer

The correct absolute value function equivalent to the given piecewise function is $f(x)=|x+4|-14$. This is because the absolute value function shifts the vertex of the V-shaped graph to $-4$ on the x-axis (matching the piecewise condition of changing behavior at $x = -4$) and adjusts the output value to align with the piecewise outputs. The "-14" adjustment ensures that the function matches the outputs of the piecewise function for values of $x$ both less than and greater than $-4$.

Write an Absolute Value Function That Is Equivalent to the Given