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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).

2 Answers

4 votes
Two last answers are correct
User Mr Punch
by
7.8k points
3 votes

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).

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 )

User TheMonkeyMan
by
8.2k points

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