Question

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.

$\mathrm{f}\left(\mathrm{x}\right)=-3{\mathrm{x}}^2.$

Short answer

Domain of the function is$(-\infty ,\infty ).$Range of the function is$(-\infty ,0].$

Step-by-step solution

Step 1. Given Information

Given function is$\mathrm{f}\left(\mathrm{x}\right)=-3{\mathrm{x}}^2.$

Step 2. Formation of ordered pairs

It is not a linear function and create the table using different values of x. It can form ordered pairs. Connect and plot to create graph.

$\mathrm{x}$	$\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)$	$(\mathrm{x},\mathrm{y})$
$0$	$\mathrm{y}=-3{\left(0\right)}^2\to \mathrm{y}=0$	$(0,0)$
$-1$	$\mathrm{y}=-3{(-1)}^2\to \mathrm{y}=-3$	$(-1,-3).$
$1$	$\mathrm{y}=-3{\left(1\right)}^2\to \mathrm{y}=-3$	localid="1658558186663" $(1,-3)$
$-2$	$\mathrm{y}=-3{(-2)}^2\to \mathrm{y}=-12$	$(-2,-12)$
$2$	$\mathrm{y}=-3{\left(2\right)}^2\to \mathrm{y}=-12$	$(2,-12)$

Step 3. Graph of the function

The graph of the drawn using slope and intercept as,

Step 4. Domain and range

Given function is a quadratic function, domain of quadratic function is all real numbers. Domain of the function is$(-\infty ,\infty ).$Given function is a quadratic function and graph represent the y-positive values, range of given function is all real numbers which is greater than or equal to zero. Range of the function is $(-\infty ,0].$