Question

NEED HELP ON THIS!!!!

Which statements are true for the function y = |x| - 2? (the function is in image) Select all that apply. THERE'S MORE THAN ONE OPTION!

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).

Answer 1

The value of the function is negative from -2 to 2, so A is false. The graph is shaped like a V, so B is true. y equals 0 twice, at -2 and 2, so C is false. y is 5 twice, at -7 and 7, so D is true. The vertex, or the sharp turn, is at (0,-2), so E is true. This means your answers are B, D, and E.

Answer 2

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:

we have

`y=\left|x\right|-2`

Statements

case A) The value of the function is never negative.

The statement is false

The value of the function is negative in the interval------>
`(-2,2)`

case B) Its graph has a V-shape

The statement is true

See the graph

case C) There is only one input for which the output is
`0`

The statement is false

There are two inputs for which the output is equal to zero

For
`x=-2` and
`x=2`

case D) There are two inputs for which the output is
`5`

The statement is true

For
`x=-7` and
`x=7`

case E) The vertex of its graph is at
`(0, -2)`

The statement is true

see the graph