Question

Use the ray tool to graph f(x)=−|x−5|.First plot the endpoint of the ray, then any point on the ray.

Answer 1

Given function is

`f(x)=-|x-5|`

Set x=5, substitute x=5, we get

`f(5)=-|5-5|`

`f(5)=-|0|`
`f(5)=0`

The point (5,0) is lie on the ray.

Set x=0, and substitute x=0 in the function , we get

`f(0)=-|0-5|`

`f(0)=-|-5|`
`\text=5 since -5<0.`

`f(0)=-5`

The point (0,-5) lies on the ray.

Set x=10, and substitute in function, we get

`f(10)=-|10-5|`

`f(10)=-|5|`

`f(10)=-5`

The point (10,-5) lies on the function.

Mark these points (5,0), (0,-5), and (10,-5) and join the ray.

The graph of the given function is

When x=2,

`f(2)=-|2-5|=-3`

The point is (2,-3)

When x=8,

`f(8)=-|8-5|=-3`

The point is (8,-3).