Chapter 1.3, Problem 29E

Solution

To graph: The of a function and find its domain.

Given information:

The function is $f\left(x\right)=x^2-5$ .

Graph:

The graph of the function $f\left(x\right)=x^2-5$ is shown in Fig.1.

  

The domain of a function is the set in which the function is defined.

From the Fig. (1), it is clear that when $x\to -\infty \text{and}x\to +\infty$ the function $f\left(x\right)\to \infty$ that shows, the function $f\left(x\right)$ is defined in the interval $\left(-\infty ,\infty \right)$ .

Therefore, the domain the function $f\left(x\right)$ is $\left(-\infty ,\infty \right)$ .

Interpretation:

The graph of the function $f\left(x\right)$ is an upward open parabola with vertex $\left(0,-5\right)$ .