Defining and Writing Functions

Example 12

Reading Function Values from a Graph

Given the graph in Figure 4,

(a) Evaluate $f(2)$.

(b) Solve $f(x)=4$.

Figure 4

Solution

(a) To evaluate $f(2)$, locate the point on the curve where $x=2$, then read the $y$-coordinate of that point. The point has coordinates $(2,1)$, so $f(2)=1$. See Figure 5.

Figure 5

(b) To solve $f(x)=4$, we find the output value $4$ on the vertical axis. Moving horizontally along the line $y=4$, we locate two points of the curve with output value $4:(-1,4)$ and $(3,4)$. These points represent the two solutions to $f(x)=4:-1$ or $3$. This means $f(-1)=4$ and $f(3)=4$, or when the input is $-1$ or $3$, the output is $4$. See Figure 6.

Figure 6

Try It #8

Using Figure 4, solve $f(x)=1$.