Chapter 1.3, Problem 45E

To determine

To state: set of ordered pairs for, $y=11-x\text{ and }-3\le x\le 0$ , and state whether the relation is a function.

Answer to Problem 45E

Relation = $\left\{\left(-1,12\right),\left(-2,13\right),\left(-3,14\right)\right\}$

The relation is a function.

Explanation of Solution

Given information:

The given equation and domain is as follows:

  $y=11-x\text{ and }-3\le x\le 0$ , where x is an integer.

Calculation:

The three values of x are as follows:

  $\begin{array}{l}{x}_1=-1\\ x_2=-2\\ x_3=-3\end{array}$

Put $x_1$ in the equation and evaluate $y_1$ as follows:

  $\begin{array}{c}{y}_1=11-x_1\\ =11-\left(-1\right)\\ =11+1\\ =12\end{array}$

Put $x_2$ in the equation and evaluate $y_2$ as follows:

  $\begin{array}{c}{y}_2=11-x_2\\ =11-\left(-2\right)\\ =11+2\\ =13\end{array}$

Put $x_3$ in the equation and evaluate $y_3$ as follows:

  $\begin{array}{c}{y}_3=11-x_3\\ =11-\left(-3\right)\\ =11+3\\ =14\end{array}$

Therefore, the set ordered pairs $\left[\left(x_1,y_1\right),\left(x_2,y_2\right)\text{ and }\left(x_3,y_3\right)\right]$ is $\left\{\left(-1,12\right),\left(-2,13\right),\left(-3,14\right)\right\}$ .

The line equation can be rewritten as slope intercept form as follows:

  $\begin{array}{l}y=mx+b\\ y=-x+11\end{array}$

In this equation the slope is negative. Hence, this relation is a function