Question

The graph of h(x) = l x - 10 l + 6 is shown. On which interval is this graph increasing?

A. (–∞, 6)
 B. (–∞, 10)
 C. (6, ∞)
 D. (10, ∞)

Answer 1

D
From point (10,6) to the right

Answer 2

we have

`h\left(x\right)=\left|x-10\right|+6`

we know that

see the graph

Let

`A(0,16)\\ B(10,6)\\ C(20,16)`

Find the slope BC

`m=((y2-y1))/((x2-x1))`

`m=((16-6))/((20-10))`

`m=((10))/((10))`

`m=1`

The slope is positive

so

The graph is increasing in the interval----------> (10, ∞)

Find the slope AB

`m=((y2-y1))/((x2-x1))`

`m=((6-16))/((10-0))`

`m=((-10))/((10))`

`m=-1`

The slope is negative

so

The graph is decreasing in the interval----------> (-∞,10)

therefore

the answer is the option

D. (10, ∞)