Chapter 1.1, Problem 38E

To determine

To find: The domain and range of the function and sketch the graph.

Explanation of Solution

Given information:

The given function is,

  $H\left(t\right)=\frac{4-t^2}{2-t}$

Consider the given function,

  $H\left(t\right)=\frac{4-t^2}{2-t}$

The above equation is valid for all real number except,

  $\begin{array}{l}2-t\ne 0\\ t\ne 2\end{array}$

Thus, the domain of the given function is all real numbers except $t\ne 2$ .

Consider the graph of the given function,

  

The range of the given function is all real numbers except $H\left(t\right)\ne 4$.