Question

What is the range of the function g(x) = |x – 12| – 2?.

Answer 1

The range of the given function is [-2,∞).

what is the range of a function?

the range is the complete set of all possible values of the dependent variable say 'y'.

given function is:  f(x)=  |x – 12| – 2

f(x) = x-14  ∀ x≥12

f(x) = -x+10 ∀ x < 12

value of the above function at x=12 will be -2 means the minimum value of the function will be -2.

now, from the graph, we can see that f(x) is leading to infinity

so the range will be [-2,∞).

therefore, The range of the given function is [-2,∞).

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Answer 2

The range of the function is all real number of input value (y-value) grater than or equal to -2.

What is range of function?

Range of a function is the set of all the possible output values which are valid for that function.

The function given in the problem is,

$g(x) = |x - 12| - 2$

Lets, compare the above function with the vertex form of the absolute function. The vertex form of the absolute function with vertex (h, k) can be given as,

$y=a|x-h|+k$

On comparing the vertex form with the given equation, we get,

$h=12\\k=-2$

Now, as the tange of a function is the set of all the possible output values which are valid for that function.

Here, the function does not take the value which are less than -2. Hence, the range of the function is all real number of input value (y-value) grater than or equal to -2.

Learn more about the range of the function here;

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