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{ Use |-5|=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).