Question

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

$\mathrm{f}\left(\mathrm{x}\right)=2\sqrt{\mathrm{x}}$

Short answer

Domain of the function is $[0,\infty )$and range of the function is$[0,\infty ).$

Step-by-step solution

Step 1. Given Information

Given that the equation is$\mathrm{f}\left(\mathrm{x}\right)=2\sqrt{\mathrm{x}}$

Step 2. Formation of ordered pairs

The table can be created by different x-values. It's not a linear function. It can form ordered pairs by plot and connect to form a graph.

$\mathrm{x}$	$\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)$	$(\mathrm{x},\mathrm{y})$
$0$	$\mathrm{y}=2\sqrt{0}\to \mathrm{y}=0$	$(0,0)$
$4$	$\mathrm{y}=2\sqrt{4}\to \mathrm{y}=4$	$(4,4)$
$9$	$\mathrm{y}=2\sqrt{9}\to \mathrm{y}=6$	$(9,6)$
$1$	$\mathrm{y}=2\sqrt{1}\to \mathrm{y}=2$	$(1,2)$

Step 3. Graph of the function

The graph can be drawn as,

Step 4. Domain and Range

Given function is a square root function, the domain of the square root function is the value set at the argument is non-zero. Domain of the function is $[0,\infty )$. Given function is a square root function whose graph has y-positive values, the range is all real numbers which is equal to or greater than zero. The range of the function is $[0,\infty ).$