Find the largest open interval where the function is changing as requested.
-Decreasing $f ( x ) = | x - 8 |$
A) $( - \infty , - 8 )$
B) $( 8 , \infty )$
C) $( - 8 , \infty )$
D) $( - \infty , 8 )$

Question

Quizplus · Accepted Answer

The function is only defined for $x \geq 0$ since there is an absolute value. Therefore, the only possible interval where the function could be decreasing is $(8, \infty)$. However, on this interval, the function is actually increasing since as $x$ gets further away from 8, the absolute value term gets larger. Therefore, the largest open interval where the function is decreasing is $(-\infty, 8)$.

Find the Largest Open Interval Where the Function Is Changing f(x)=∣x−8∣f ( x ) = | x - 8 |f(x)=∣x−8∣

Find the Largest Open Interval Where the Function Is Changing $f ( x ) = | x - 8 |$