The domain of given function f(x) is {x | -4 < x ≤ 4}
What is the step function?
"It is a piecewise-defined function in which every piece is a horizontal line segment or a point."
What is domain of function?
"It is the set of value for which the function is well defined."
For given question,
The left-most segment goes from (-4, 1) to (-2, 1).
The right-most segment goes from (2, 4) to (4, 4).
From the graph of step function,
we can observe that a function f(x) takes input value (x-coordinate value) from -4 to 4.
But there is open circle at -4.
This means a function does not take the value x = -4, but all values which are greater than -4.
Therefore, the domain of given function f(x) is {x | -4 < x ≤ 4}
Learn more about the domain of a function here:
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