What is the range of the function g(x) = |x – 12| – 2? a). {y | y > –2} b). {y | y > –2} c). {y | y > 12} d). {y | y > 12}

Step-by-step explanation:

The function is given by

It is an absolute value function which has a v- shaped graph.

The vertex form of an absolute function is given by y = a|x-h| +k, where (h,k) is the vertex.

Comparing the given equation with this, we have

h = 12

k = -2

Hence, the vertex would be (12,-2).

Now, the range of the function is the set of y values for which the function is defined.

This function has vertex of (12,-2). hence, it would not be take any values which are less than -2. Please see the attache graph.

Hence, the range would be the all y values greater than or equal to -2.

Hence, range is given by

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

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step-by-step explanation: