Question

the step function f(x) is graphed.
what is the value of f(-1)?
options: -3, -1, 0, 1

Explanation:

Step1: Identify the interval for \( x = -1 \)

In a step function, we look at the graph to see which interval \( x = -1 \) falls into. The graph has a closed dot (filled circle) at \( x = -1 \) and an open dot at \( x = 1 \) for the segment where \( y = -1 \)? Wait, no, let's check the coordinates. Wait, the point at \( x = -1 \): looking at the graph, the segment that includes \( x = -1 \) has a closed dot at \( x = -1 \) (since it's filled) and goes to \( x = 1 \) (open dot). The \( y \)-value for this segment: looking at the graph, the horizontal line at \( y = -1 \)? Wait, no, the first segment (leftmost) is at \( y = -3 \) from \( x = -4 \) to \( x = -2 \) (open dot at \( x = -2 \)), then from \( x = -2 \) (closed dot?) Wait, no, the graph: at \( x = -1 \), the closed dot is at \( (-1, -1) \)? Wait, no, let's re-examine. The graph: the horizontal line with closed dot at \( x = -1 \) (the point \( (-1, -1) \) is a closed dot) and open dot at \( x = 1 \) (so the interval is \( -1 \leq x < 1 \)) with \( y = -1 \)? Wait, no, the options are -3, -1, 0, 1. Wait, the closed dot at \( x = -1 \): looking at the graph, the segment that includes \( x = -1 \) has \( y = -1 \)? Wait, no, maybe I misread. Wait, the first segment (left) is from \( x = -4 \) to \( x = -2 \) (open dot at \( x = -2 \)) with \( y = -3 \) (closed dot at \( x = -4 \), open at \( x = -2 \)). Then from \( x = -2 \) (closed dot?) Wait, no, the next segment: at \( x = -1 \), the closed dot is at \( (-1, -1) \), and open dot at \( x = 1 \), so \( y = -1 \) for \( -1 \leq x < 1 \). Wait, but the options include -1. Wait, no, wait the options: -3, -1, 0, 1. Wait, maybe I made a mistake. Wait, the graph: the horizontal line with closed dot at \( x = -1 \) (the point \( (-1, -1) \)) and open dot at \( x = 1 \), so \( f(-1) \) is the \( y \)-value at \( x = -1 \), which is -1? Wait, no, the options have -1 as an option. Wait, let's check again. The closed dot at \( x = -1 \): looking at the graph, the \( y \)-coordinate for \( x = -1 \) is -1 (since the closed dot is at \( (-1, -1) \)), so \( f(-1) = -1 \)? Wait, no, maybe the segment is \( y = -1 \) from \( x = -1 \) (closed) to \( x = 1 \) (open). So when \( x = -1 \), the function value is -1.

Step2: Confirm the value

Since the closed dot at \( x = -1 \) is on the line where \( y = -1 \), the value of \( f(-1) \) is -1.

Answer:

-1 (corresponding to the option: -1)