the graph of h(x)=|x - 10|+6 is shown. on which interval is this graph increasing? (-∞,6) (-∞,10) (6,∞) (10,∞)
the graph of h(x)=|x - 10|+6 is shown. on which interval is this graph increasing? (-∞,6) (-∞,10) (6,∞) (10,∞)
Answer
Explanation:
Step1: Recall absolute - value function property
The general form of an absolute - value function is (y = a|x - h|+k). For the function (h(x)=|x - 10|+6), the vertex is at the point ((h,k)=(10,6)).
Step2: Analyze the behavior of the absolute - value function
The absolute - value function (y = |x - 10|+6) can be written as a piece - wise function: (h(x)=\begin{cases}x - 10+6=x - 4, & x\geq10\-(x - 10)+6=-x + 16, & x<10\end{cases}). The slope of (y=-x + 16) for (x < 10) is (-1) (decreasing), and the slope of (y=x - 4) for (x\geq10) is (1) (increasing).
Answer:
D. ((10,\infty))