evaluate the function graphically.\nfind $f(3)$

Answer

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:

Find ( x = 3 ) on the x - axis.
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 )