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Which statements are true for the function y = |x| - 2? Select all that apply.


The value of the function is never negative.

Its graph has a V-shape.

There is only one input for which the output is 0.

There are two inputs for which the output is 5.

The vertex of its graph is at (0, -2).

Verified Answer :

kubzab

Two last answers are correct

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,

\(y=|x|-2\) ------(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  \([-2, \infty)\)

So, the value of the function can be negative,

Now, for y = 0,

\(\implies 0 = |x|-2\)

\(\implies |x|=2\implies x =\pm 2\)

Thus, there are two inputs for which the output is 0,

Also, for y = 5,

\(\implies 5=|x|-2\)

\(\implies |x|=7\implies x = \pm 7\)

Thus, there are two inputs for which the output is 5,

Since, if an absolute function is,

\(y=a|x-h|+k\) ------(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 )

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