Question

"The graph represents

y=⌈x⌉+1.

On a coordinate plane, a step graph consists of horizontal segments, each 1 unit long. The left end of each segment is an open circle, and the right end is a closed circle. The left-most segment extends from (−5,−3) to
(−4,−3). Each subsequent segment is 1 unit higher and 1 unit farther to the right than the previous one. The right-most segment goes from (3,5) to (4,5).

What is
f(−2.75)?

A)
−
5


B)
−
4


C)
−2

D)
−1"

Answer 1

The value of f(-2.75) for the step function y=⌈x⌉+1 is 1, as -2.75 rounds up to -2 and the corresponding y-value of the segment starting at x = -3 is 0, to which we add 1.

Step-by-step explanation:

The student's question involves finding the value of f(-2.75) for the function y=⌈x⌉+1, where ⌈x⌉ represents the ceiling function, which rounds x up to the nearest integer. Given that the graph consists of horizontal segments that represent this ceiling function, the value at x = -2.75 falls on the segment that extends from (-3,0) to (-2,1), since the x-values are rounded up to the next integer. Therefore, for x = -2.75, the function value is at the height of the start of this segment, which is 0, plus 1, making f(-2.75) = 1.