Question

In the following exercises, a). graph each function b). state its domain and range. Write the domain and range in interval notation.

$f\left(x\right)=-\frac{1}{2}{x}^2$

Short answer

(a).The graph of the solution is

b). The domain interval notation is $[-3,3]$

The range interval notation is$\left[-\frac{9}{2},-\frac{9}{2}\right]$

Step-by-step solution

Part a). Given Information

$f\left(x\right)=-\frac{1}{2}{x}^2$

Part (a) Step 1. Graph of the function

Part (b) Step 1. Domain of the function

This is function has a value when $x$is from$-3$to $3$. Therefore, its domain interval notation is$[-3,3]$

Part (b) Step 2. Range of the function

This is function value, or $y-$value $-\frac{9}{2}$. Therefore, the range in interval notation is$\left[-\frac{9}{2},-\frac{9}{2}\right]$