The graph of the step function g (x) = - ⌊x⌋ + 3 is shown. On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, 5) to (negative 1, 5). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, negative 1) to (5, negative 1). What is the domain of g (x) ? x x x - 1 ≤ x ≤ 5

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Step-by-step explanation:

There is a box function plotted on the graph.

The function is g (x) = - ⌊x⌋ + 3.

Now, we know that a box function represents a step graph having horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle.

It is given that the left-most segment of the given graph goes from (-2,5) to (-1,5) and the rightmost segment goes from (4,-1) to (5,-1).

So, for the left most segment the domain is - 2 ≤ x < - 1

And for the right most segment the domain is 4 ≤ x < 5

Therefore, the total domain of g (x) will be - 2 ≤ x < 5 (Answer)

Answer: - 2 ≤ x < 5

Step-by-step explanation: It is given that the left-most segment of the given graph goes from (-2,5) to (-1,5) and the rightmost segment goes from (4,-1) to (5,-1).

So, for the left most segment the domain is - 2 ≤ x < - 1

And for the right most segment the domain is 4 ≤ x < 5

Therefore, the total domain of g (x) will be - 2 ≤ x < 5 (Answer)