Question

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 is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}

Answer 1

Answer:

{x| –2 ≤ x < 5}

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  {x| –2 ≤ x < 5} (Answer)

Answer 2

Answer: {x| –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  {x| –2 ≤ x < 5} (Answer)