Question

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

Explanation:

Step1: Locate x=3 on x - axis

Find the position of \( x = 3 \) on the horizontal (x - axis) of the graph.

Step2: Determine the corresponding y - value

From \( x = 3 \), move vertically to the point on the graph. The open circle at \( x = 3 \) is a discontinuity, but the solid dot (the actual function value at \( x = 3 \)) is at \( y=-4 \)? Wait, no, wait. Wait, the graph: when \( x = 3 \), the solid dot is at \( y=-4 \)? Wait, no, let's re - examine. Wait, the line: when \( x = 3 \), the open circle is at \( y = 3 \), but the solid dot (the function's value at \( x = 3 \)) is the filled point. Wait, no, in piece - wise functions, the solid dot represents the actual value. Wait, looking at the graph, at \( x = 3 \), the filled dot is at \( y=-4 \)? Wait, no, maybe I misread. Wait, the x - axis: 3 is at the third grid from 0 on the right. The y - axis: the filled dot at \( x = 3 \) is at \( y=-4 \)? Wait, no, let's check the coordinates. The x - coordinate is 3, and the y - coordinate of the solid dot (the function's value at \( x = 3 \)) is - 4? Wait, no, maybe I made a mistake. Wait, the open circle is at (3,3), but the solid dot is at (3, - 4). So when we evaluate \( f(3) \), we look at the solid dot (the defined point) at \( x = 3 \), which has a y - value of - 4? Wait, no, that seems odd. Wait, maybe the graph is a piece - wise function where at \( x = 3 \), the function takes the value of the solid dot. So to find \( f(3) \), we find the point on the graph where \( x = 3 \). The solid dot (the filled circle) at \( x = 3 \) has a y - coordinate of - 4? Wait, no, let's count the grids. The x - axis: each grid is 1 unit. The y - axis: each grid is 1 unit. At \( x = 3 \), the solid dot is 4 units below the x - axis, so \( y=-4 \). Wait, but the open circle is at \( y = 3 \), but the function's value at \( x = 3 \) is the solid dot. So \( f(3)=-4 \)? Wait, no, maybe I messed up. Wait, let's start over. To evaluate \( f(3) \) graphically, we:

1. Find \( x = 3 \) on the x - axis.
2. Move up or down vertically until we hit the graph (the solid dot, since the open dot is a hole). The solid dot at \( x = 3 \) is at \( y=-4 \). So \( f(3)=-4 \).

Answer:

\( f(3)=-4 \)