Question

the step function f(x) is graphed. what is the value of f(0)? -2 -1 0 1

Explanation:

Step1: Identify x=0 on graph

Locate the point where \( x = 0 \) on the x - axis of the step - function graph.

Step2: Check the filled dot at x=0

In a step - function graph, a filled dot (solid circle) at a particular x - value indicates the value of the function at that x - value. Looking at the graph, at \( x = 0 \), the filled dot is at \( y=-2 \)? Wait, no, wait. Wait, let's re - examine. Wait, the graph: when x = 0, the step where x=0 is part of the interval. Wait, no, let's look again. Wait, the vertical line at x = 0: the filled dot is at y=-2? Wait, no, the options have - 2 as an option. Wait, no, wait the graph: let's see the steps. Wait, the step that includes x = 0: the solid dot at x = 0 is at y=-2? Wait, the options are - 2, - 1, 0, 1. Wait, maybe I made a mistake. Wait, let's check the graph again. The step function: for x in [0,1), what's the value? Wait, no, at x = 0, the solid dot is at y=-2? Wait, the graph shows that at x = 0, the filled circle is at y=-2. Wait, but let's confirm the step function's definition. A step function has intervals where it is constant. At x = 0, we look for the interval that contains x = 0. The interval for the step that includes x = 0: the left - closed interval (since filled dots are included). So at x = 0, the function value is the y - value of the filled dot at x = 0. Looking at the graph, at x = 0, the filled dot is at y=-2? Wait, no, wait the graph: the vertical line x = 0, the solid dot is at (0, - 2). So f(0)=-2? Wait, but let's check the options. The first option is - 2.

Step1: Locate x = 0 on the x - axis.

Find the point on the graph where \( x = 0 \).

Step2: Determine the y - value at x = 0.

At \( x = 0 \), the filled (solid) dot on the step - function graph corresponds to \( y=-2 \). This is because in a step - function, solid dots represent the included endpoints of the intervals, so we use the y - value of the solid dot at \( x = 0 \).

Answer:

-2 (corresponding to the option with - 2, i.e., the first option: \(\boldsymbol{-2}\))