complete the statements for the graph of f(x) = |x|. the domain of the function is. the range of the…

Explanation:

Step1: Define domain

The domain of a function is the set of all possible input - values. For (y = |x|), (x) can be any real number. So the domain is ((-\infty,\infty)).

Step2: Define range

The absolute - value function (y = |x|) always gives a non - negative output. That is, (y\geq0). So the range is ([0,\infty)).

Step3: Analyze interval ((0,\infty))

For (x\in(0,\infty)), as (x) increases, (y = |x|=x) also increases. So the graph is increasing on the interval ((0,\infty)).

Step4: Analyze interval ((-\infty,0))

For (x\in(-\infty,0)), as (x) increases (moves towards 0), (y = |x|=-x) decreases. So the graph is decreasing on the interval ((-\infty,0)).

Answer:

The domain of the function is ((-\infty,\infty)). The range of the function is ([0,\infty)). The graph is increasing over the interval ((0,\infty)). The graph is decreasing over the interval ((-\infty,0)).