Question

evaluate the function graphically.
find ( f(1) )

Explanation:

Step1: Understand the graph

The graph shows a piece - wise function. To find \(f(1)\), we look at the \(x\) - value of 1 on the \(x\) - axis and then find the corresponding \(y\) - value on the graph.

Step2: Locate \(x = 1\) on the graph

We find the vertical line \(x = 1\) and then see which point on the graph lies on this vertical line. From the graph, when \(x = 1\), we follow the graph's segment. The first segment starts at \(x = 0\) (open circle at \((0,7)\)) and goes down. At \(x=1\), we are on the segment that starts from \((0,7)\) (open circle) and goes towards the next point. By looking at the graph, when \(x = 1\), we can see that the \(y\) - value is determined by the linear segment. The slope of the segment from \((0,7)\) to \((4,3)\) (open circle) can be calculated as \(m=\frac{3 - 7}{4-0}=\frac{- 4}{4}=-1\). The equation of the line using point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(0,7)\) is \(y-7=-1(x - 0)\), or \(y=-x + 7\). When \(x = 1\), \(y=-1 + 7=6\). Also, by directly looking at the graph, the point corresponding to \(x = 1\) on the graph (the segment that includes \(x = 1\)) has a \(y\) - value of 6.

Answer:

\(f(1)=6\)