Answer: The correct options are,
Its graph has a V-shape.
There are two inputs for which the output is 5.
The vertex of its graph is at (0, -2).
Step-by-step explanation:
Here, the given function is,
[tex]y=|x|-2[/tex] ------(1)
Which is an absolute function,
Since, the graph of an absolute function is always V shaped,
⇒ The graph of the given function is V-shaped,
Also, the range of the function is [tex][-2, \infty)[/tex]
So, the value of the function can be negative,
Now, for y = 0,
[tex]\implies 0 = |x|-2[/tex]
[tex]\implies |x|=2\implies x =\pm 2[/tex]
Thus, there are two inputs for which the output is 0,
Also, for y = 5,
[tex]\implies 5=|x|-2[/tex]
[tex]\implies |x|=7\implies x = \pm 7[/tex]
Thus, there are two inputs for which the output is 5,
Since, if an absolute function is,
[tex]y=a|x-h|+k[/tex] ------(2)
Then, the vertex of the function is (h,k),
By comparing equation (1) and (2),
The vertex of the given function is, (0, -2 )
