Question

The step function f(x) is graphed.

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, 3) to (negative 4, 3). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (2, negative 4) to (3, negative 4).

What is the value of f(0)?

-2
-1
0
1

Answer 1

To find the value of f(0), determine which segment contains the x-coordinate 0 and find the y-coordinate of that segment.

Step-by-step explanation:

The step function f(x) is graphed with horizontal segments that are each 1 unit long. The left end of each segment is a closed circle, and the right end is an open circle. The left-most segment goes from (-5,3) to (-4,3). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (2,-4) to (3,-4).

To find the value of f(0), we need to determine which segment contains the x-coordinate 0. Since the left-most segment starts at -5 and ends at -4, it does not include 0. The second segment starts at -4 and ends at -3, so it also does not include 0. The third segment starts at -3 and ends at -2, which includes 0. Therefore, the value of f(0) is the y-coordinate of the third segment, which is 2 units below the previous segment. Since the previous segment is at y = 3, the value of f(0) is 3 - 2 = 1.