Chapter 2.2, Problem 36AYU

To determine

To explain: the procedure of finding the domain and range of a function from its graph and from its equation.

Explanation of Solution

Let them be $x_{\min }$ and $x_{\max }$ respectively. If the function is continuous between be $x_{\min }$ and $x_{\max }$ , then the domain will be $\left\{x|x_{\min }\le x\le x_{\max }\right\}$ .

If there are discontinuities you have to subtract the set of discontinuities from the above domain.

To determine the range of a function $f\left(x\right)$ from its graph, find the minimum and maximum values of $y$ from the graph. Let them be $y_{\min }$ and $y_{\max }$ , then the range will be

  $\left\{y|y_{\min }\le y\le y_{\max }\right\}$ .

If there are discontinuities you have to subtract the set of discontinuities from the above range.

To determine the domain of a function $f\left(x\right)$ from its equation determine the set of values $x$ can take so that $f\left(x\right)$ will be real number. Eliminate the $x$ values that results in division by zero from the domain.

To determine the range of a function $f\left(x\right)$ from its equation find the set of all possible $y$ values that results from the domain of $f\left(x\right)$ .