Chapter 1.4, Problem 34E

To determine

To state: set of ordered pairs and also tell whether this relation is a function.

Answer to Problem 34E

  $\left\{\left(-4,16\right),\left(-3,9\right),\left(-2,4\right)\right\}$

This relation is a function.

Explanation of Solution

Given information: The given equation and domain restriction are as follows:

  $\begin{array}{l}y=x^2\\ -4\le x\le -2\end{array}$

Calculation The possible values of x are as follows:

  $\begin{array}{l}{x}_1=-4\\ x_2=-3\\ x_3=-2\end{array}$

Substitute these values in the given equation and solve to get the corresponding value of y.

  $\begin{array}{l}{y}_1={\left(x_1\right)}^2={\left(-4\right)}^2=16\\ y_2={\left(x_2\right)}^2={\left(-3\right)}^2=9\\ y_3={\left(x_3\right)}^2={\left(-2\right)}^2=4\end{array}$

Thus the set of three ordered pairs are $\left\{\left(-4,16\right),\left(-3,9\right),\left(-2,4\right)\right\}$ .

Since, no two ordered pairs have same first element. Therefore, this relation is a function.