Chapter 1.5, Problem 7E

To determine

To calculate: Use the graph of the function to find the domain and range of f and each function value.

  $\left(a\right)f\left(-1\right)\left(b\right)f\left(0\right)\left(c\right)f\left(1\right)\left(d\right)f\left(2\right)$

  

Answer to Problem 7E

  $\begin{array}{l}f\left(-1\right)=-1\\ f\left(0\right)=0\\ f\left(1\right)=-1\\ f\left(2\right)=8\end{array}$

Explanation of Solution

Domain is the set of all values of x for which the function is defined. From the graph, we can see that x varies from $-2$ to 2 i.e. $x\in \left(-2,2\right]$

Range is the set of all values of y which the function can take. From the graph, we can see that the value of y varies from $-1$ to 8 i.e. $y\in \left[-1,8\right]$

Finding $f\left(-1\right)$ , from the graph we can see that $y=-1$ when $x=-1$ , as point $\left(-1,-1\right)$ lies on the graph.

So, $f\left(-1\right)=-1$

Finding $f\left(0\right)$ , from the graph we can see that $y=0$ when $x=0$ , as point $\left(0,0\right)$ lies on the graph.

So $f\left(0\right)=0$

Finding $f\left(1\right)$ , from the graph we can see that $y=-1$ When

  $x=1$ , as point $\left(1,-1\right)$ lies on the graph.

So $f\left(-1\right)=-1$

Finding $f\left(2\right)$ , from the graph we can see that $y=8$ when $x=2$ , as point $\left(2,8\right)$ lies on the graph.

So $f\left(2\right)=8$