Chapter 8.4, Problem 44HP

To determine

To write the difference between the graph of $f\left(x\right)\text{ and g}\left(x\right)$

Answer to Problem 44HP

The difference between the graphs of $f\left(x\right)\text{ and g}\left(x\right)$ is that, $f\left(x\right)$ is a linear function while $g\left(x\right)$ is a rational function and $f\left(x\right)$ is continuous while $g\left(x\right)$ has a point discontinuity that is a hole at $x=-3$

Explanation of Solution

Given information:

  $f\left(x\right)=x-2\text{ and }g\left(x\right)=\frac{\left(x+3\right)\left(x-3\right)}{x+3}$

The difference between the graphs of $f\left(x\right)\text{ and g}\left(x\right)$ can be written by the use of its given value.

From the values it clear that $f\left(x\right)$ is a linear function and $g\left(x\right)$ is a rational function, this is the first difference.

And also $f\left(x\right)$ is continuous while $g\left(x\right)$ has a point discontinuity that is a hole at $x=-3$ . Even though the $x+3$ factors cancel, but still $x=-3$ is excluded from the domain of the function.