Chapter 1.2, Problem 6E

(a)

To determine

To find:The domain and range of the function $y=x^2-9$ .

Answer to Problem 6E

The domain and range of the function $y=x^2-9$ is $\left(-\infty ,\infty \right)$ and $\left[-9,\infty \right)$ respectively.

Explanation of Solution

Given information:The given function is $y=x^2-9$ .

Calculation:

The function $y=x^2-9$ is defined for all the real values of $x$ .So, the domain of the function $y=x^2-9$ is the set of real numbers or the interval $\left(-\infty ,\infty \right)$ .

The function $x^2$ is always positive for all the real values of $x$ . So,

  $x^2>0$

Subtract $9$ from both sides.

  $\begin{array}{c}{x}^2-9>0-9\\ y>-9\end{array}$

So, the range of the function $y=x^2-9$ is the interval $\left[-9,\infty \right)$ .

Therefore, the domain and range of the function $y=x^2-9$ is $\left(-\infty ,\infty \right)$ and $\left[-9,\infty \right)$ respectively.

(b)

To determine

To graph:The function $y=x^2-9$ .

Explanation of Solution

Given information:The function is $y=x^2-9$ .

Graph:

The graph of the function $y=x^2-9$ is shown below:

  

Figure(1)

Interpretation:The graph of the function $y=x^2-9$ is an upwards parabola with vertex at the point $\left(0,-9\right)$ .