Question

The step function f(x) is graphed.

On a coordinate plane, a step graph has horizontal segments that are each 2 units 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 3, negative 3) to (negative 1, negative 3). Each segment is 2 units higher and 2 units farther to the right than the previous segment. The right-most segment goes from (3, 3) to (5, 3).

What is the value of f(−1)?

-3
-1
0
1

Answer 1

Based on the graph of the step function f(x) shown below, the value of f(−1) include the following: B. -1.

In Mathematics and Euclidean Geometry, a piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Note: The inequality symbol < or > represents a hollow dot (circle).

The inequality symbol ≤ or ≥ represents a solid dot (circle).

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the given piecewise-defined function, we have the following domains;

Domain = -2 ≤ x < -1, for f(x) = -3.

Domain = -1 ≤ x < 1, for f(x) = -1.

Domain = 1 ≤ x < 3, for f(x) = 1

Domain = 3 ≤ x < 5, for f(x) = 3.

Since the second interval [-1, 1) is closed at -1 but open at 1, it implies that the function is defined for -1. Therefore, the value of f(−1) is given by;

f(−1) = -1

Complete Question;

The step function f(x) is graphed.

What is the value of f(−1)?

-3

-1

0

1