select the correct answer.\non what interval is the function h(x) = |x - 5| + 2 increasing?\na. (2, ∞)\nb…

select the correct answer.\non what interval is the function h(x) = |x - 5| + 2 increasing?\na. (2, ∞)\nb. (5, ∞)\nc. (-∞, 2)\nd. (-∞, 5)

select the correct answer.\non what interval is the function h(x) = |x - 5| + 2 increasing?\na. (2, ∞)\nb. (5, ∞)\nc. (-∞, 2)\nd. (-∞, 5)

Answer

Answer:

B. $(5, \infty)$

Explanation:

Step1: Rewrite absolute - value function

The absolute - value function $h(x)=|x - 5|+2$ can be written as a piece - wise function: [h(x)=\begin{cases}x - 5+2=x - 3, & x\geq5\-(x - 5)+2=-x + 7, & x<5\end{cases}]

Step2: Analyze the slope of each part

For $y=x - 3$ ($x\geq5$), the slope $m = 1>0$, so it is increasing. For $y=-x + 7$ ($x<5$), the slope $m=-1<0$, so it is decreasing. So the function $h(x)=|x - 5|+2$ is increasing on the interval $(5,\infty)$.