Chapter 8, Problem 1RE

To determine

The domain and range of $\left\{\left(\frac{1}{3},10\right),\left(6,-\frac{1}{2}\right),\left(\frac{1}{4},4\right),\left(7,\frac{2}{5}\right)\right\}$.

Answer to Problem 1RE

Solution:

The domain and range are $\underset{\_}{\left\{\frac{1}{3},6,\frac{1}{4},7\right\}\text{ and}\left\{10,-\frac{1}{2},4,\frac{2}{5}\right\}}$ respectively.

Explanation of Solution

Given information:

The function is $\left\{\left(\frac{1}{3},10\right),\left(6,-\frac{1}{2}\right),\left(\frac{1}{4},4\right),\left(7,\frac{2}{5}\right)\right\}$.

Consider the function value is:

$\left\{\left(\frac{1}{3},10\right),\left(6,-\frac{1}{2}\right),\left(\frac{1}{4},4\right),\left(7,\frac{2}{5}\right)\right\}$

The domain of the function must contain the $x$ values therefore,

$\text{Domain:}\left\{\frac{1}{3},6,\frac{1}{4},7\right\}$

The range of the function must contain the $y$ values therefore,

$\text{Range}\text{:}\left\{10,-\frac{1}{2},4,\frac{2}{5}\right\}$