Question

The graph represents y = ⌈x⌉ + 1.

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 3) to (negative 4, negative 3. Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (3, 5) to (4, 5).
What is f(–2.75)?

–5
–4
–2
–1

Answer 1

Do you understand how a floor function works? Pay attention to the vertical shift

Answer 2

First evaluate the floor part of the function

y=floor(-2.75) + 1

Remember for floor you go for the nearest integer less than the value. Whereas, in ceiling functions, you go to the nearest integer above the value.

So floor(-2.75) = -3, correct? (likewise for ceiling it's -1)

Now you can add +1 to that because the function is y=floor(x)+1