Question

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

Answer 1

see the attachment

Explanation:

The ceiling of numbers between -1 and 0 (not including -1) will be 0. Adding 3 to that moves the segment up to y = 3. Hence, the last graph is the appropriate one.

Any integer is its own ceiling, and it is also the ceiling of numbers between that and the next lower integer. Hence each segment on the graph will have an open circle at the left end and a closed circle at the right end.