Appendix C - Functions - Page 436: 59

(a) $f(-2)=-3$ (b) $f(0)=-2$ (c) $f(1)=0$ (d) $f(4)=2$

(a) To evaluate $f(-2)$ using the graph, we first find $-2$ on the x-axis. From $-2$ on the x-axis, we move down vertically until the graph of $f$ is reached. From this point, we then move horizontally towards the y-axis which gives a corresponding value of $-3$. Therefore, $f(-2)=-3$. (b) To evaluate f(0) using the graph, we find $0$ on the x-axis. From $0$ on the x-axis, we move down vertically until the graph of f is reached. This point represents the required y-component. Therefore, $f(0)=-2$. (c) To evaluate $f(1)$ using the graph, we find $1$ on the x-axis. Since the graph passes through x=1, the y-component of this point is the required answer. The y-component of any point lying on the x-axis is $0$. Therefore, $f(1)=0$. (d) To evaluate $f(4)$ using the graph, we find $4$ on the x-axis. From $4$ on the x-axis, we move up vertically until the graph of $f$ is reached. From this point, we then move horizontally towards the y-axis which gives a corresponding value of $2$. Therefore, $f(4)=2$.