Question

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

Explanation:

Step1: Locate x = -1 on the graph

Find the point on the x - axis corresponding to \( x=-1 \).

Step2: Determine the y - value at x = -1

For a step function, we look at the closed dot (filled circle) at \( x = - 1 \). The y - coordinate of the closed dot at \( x=-1 \) is - 1? Wait, no, looking at the graph: the interval around \( x=-1 \), the closed dot is at \( y=-1 \)? Wait, no, let's re - examine. The graph: at \( x=-1 \), the closed dot is on the line where \( y=-1 \)? Wait, no, the first segment (from left) has a closed dot at \( x=-4 \) (or so) with \( y = - 3 \), then a closed dot at \( x=-2 \)? Wait, no, the x - axis: the points are at \( x=-1 \), the closed dot is at \( y=-1 \)? Wait, no, looking at the grid: the x - value of - 1, the closed dot is at \( y=-1 \)? Wait, no, the graph shows that at \( x=-1 \), the closed dot is on the horizontal line with \( y=-1 \)? Wait, no, let's check the coordinates. The x - axis is marked with - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6. The y - axis with - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4. At \( x=-1 \), the closed dot is at \( y=-1 \)? Wait, no, the segment from \( x=-4 \) (closed dot) to \( x=-2 \) (open dot) has \( y=-3 \)? No, wait, the first segment (leftmost) has a closed dot at \( x=-4 \) (or \( x=-3 \)?) with \( y=-3 \), then a closed dot at \( x=-2 \)? No, the x=-1: looking at the graph, the closed dot at \( x=-1 \) is on the line where \( y=-1 \)? Wait, no, the user's graph: at \( x=-1 \), the closed dot is at \( y=-1 \)? Wait, no, the options are - 3, - 1, 0, 1. Wait, let's re - look. The horizontal line with the closed dot at \( x=-1 \): the y - value is - 1? Wait, no, the first (bottom) segment: from \( x=-4 \) (closed dot) to \( x=-2 \) (open dot) with \( y=-3 \)? No, then the next segment: from \( x=-2 \) (closed dot) to \( x = 0 \) (open dot) with \( y=-1 \)? Wait, at \( x=-1 \), which is between - 2 and 0, the closed dot is at \( x=-2 \)? No, I think I made a mistake. Let's look again. The graph: at \( x=-1 \), the closed dot is at \( y=-1 \). Wait, the options are - 3, - 1, 0, 1. So when \( x=-1 \), the value of the step function \( f(-1) \) is the y - value of the closed dot at \( x=-1 \). From the graph, the closed dot at \( x=-1 \) is at \( y=-1 \). Wait, no, the options have - 1 as an option. Wait, let's check the graph again. The x=-1, the closed dot is on the line with \( y=-1 \). So \( f(-1)=-1 \)? Wait, no, the options: the second option is - 1. Wait, maybe I misread. Let's see: the step function's graph: for \( x=-1 \), the closed dot is at \( y=-1 \), so \( f(-1)=-1 \).

Answer:

-1 (the option is " - 1" or the option with - 1, which is the second option: " - 1")