Question

evaluate the function graphically.
find $f(-3)$

Explanation:

Step1: Understand the graph

The graph has a line with an open circle and a closed dot. To find \( f(-3) \), we look at the \( x \)-value of -3.

Step2: Identify the point at \( x = -3 \)

At \( x = -3 \), we check the graph. The closed dot (filled circle) at \( x = -3 \) gives the value of the function. From the graph, the \( y \)-coordinate at \( x = -3 \) (the closed dot) is -3? Wait, no, wait. Wait, the open circle is on the line, but the closed dot is below. Wait, let's re-examine. Wait, the \( x \)-axis: when \( x = -3 \), the closed dot (the black dot) is at \( y = -3 \)? Wait, no, looking at the graph, the closed dot is at \( x = -3 \), what's the \( y \)-value? Wait, the grid: let's see the coordinates. The \( x \)-axis: -9, -8, ..., -3, -2, -1, 0, 1,... The \( y \)-axis: -10, -9,...,-3, -2, -1, 0, 1,2,3,4,5,6,7,8,9,10. Wait, the closed dot is at \( x = -3 \), and the \( y \)-coordinate: looking at the graph, the closed dot is at \( y = -3 \)? Wait, no, maybe I misread. Wait, the open circle is on the line (the upper line) at \( x = -4 \)? Wait, no, the problem is to find \( f(-3) \). So at \( x = -3 \), we have a closed dot (filled circle) and an open circle? Wait, no, the open circle is at \( x = -4 \) maybe? Wait, the graph: the line goes from the left, crosses the \( x \)-axis at \( x = -9 \), then goes up, with an open circle at some \( x \), and a closed dot at \( x = -3 \) below the line. Wait, the key is: for a function, at a given \( x \), the value is the \( y \)-coordinate of the point (filled dot, since open dot means the function is not defined there). So at \( x = -3 \), the filled dot (closed circle) is at \( y = -3 \)? Wait, no, let's check the graph again. Wait, the user's graph: the \( x \)-axis has -10 to 10, \( y \)-axis -10 to 10. The closed dot is at \( x = -3 \), \( y = -3 \)? Wait, no, maybe the closed dot is at \( x = -3 \), \( y = -3 \)? Wait, no, perhaps I made a mistake. Wait, the open circle is on the line (the upper line) at \( x = -4 \) with \( y = 4 \)? No, wait, the line is increasing, starting from the left, crossing \( x = -9 \) (y=0), then going up. At \( x = -4 \), there's an open circle (so the function is not defined there as the open circle), and at \( x = -3 \), there's a closed dot (filled circle) below the line, at \( y = -3 \). So \( f(-3) \) is the \( y \)-value of the closed dot at \( x = -3 \), which is -3? Wait, no, maybe the closed dot is at \( x = -3 \), \( y = -3 \). Wait, let's confirm: to evaluate \( f(-3) \), we find the point on the graph where \( x = -3 \). The closed dot (filled circle) at \( x = -3 \) gives the value of the function, because the open circle is a discontinuity (the function doesn't take that value there). So the closed dot at \( x = -3 \) has a \( y \)-coordinate of -3? Wait, no, maybe I misread. Wait, the graph: the closed dot is at \( x = -3 \), and the \( y \)-axis: looking at the grid, the closed dot is at \( y = -3 \). So \( f(-3) = -3 \)? Wait, no, maybe the closed dot is at \( x = -3 \), \( y = -3 \). Wait, let's check again. The problem is to find \( f(-3) \), so we look at \( x = -3 \) on the graph. The filled dot (closed circle) at \( x = -3 \) is the value of the function there, so \( f(-3) = -3 \)? Wait, no, maybe the closed dot is at \( x = -3 \), \( y = -3 \). Yes, that seems right.

Answer:

\( f(-3) = -3 \)