Question

Define the function $f:R\to R$ by $y=f\left(x\right)=x^2,x\in R$. Complete the table given below by using this defintion. What is the domain and range of this function ? Draw the graph of $f$.

Answer 1

Given: $y=f\left(x\right)=x^2,x\in R$

Step 1: Completing the table
$y=f\left(x\right)=x^2$,
$f(-4)=(-4{)}^2=16,f(-3)=(-3{)}^2=9$
$f(-2)=(-2{)}^2=4$
$f(-1)=(-1{)}^2=1,f(0)=(0{)}^2=0,$
$f\left(1\right)=(1{)}^2=1$
$f\left(2\right)=(2{)}^2=4,f(3)=(3{)}^2=9$,
$f\left(4\right)=(4{)}^2=16$,

$f\left(x\right)$	-4	-3	-2	-1	0	1	2	3	4
$x^2$	16	9	4	1	0	1	4	9	16

Given: $y=f\left(x\right)=x^2,x\in R$

Step 2: Domain of the function
Domian is the values of $x$ which belong to $R$
$\therefore \text{Domin}=R$

Step 3: Range of the function
As we know $x^2$ is always greater than or equal to zero.
$\because x^2\ge 0$
And $x\in R$
$\therefore$ Range of $f=[0,\infty$)

Step 4: Drawing diagram of the function

$f\left(x\right)$	-4	-3	-2	-1	0	1	2	3	4
$x^2$	16	9	4	1	0	1	4	9	16

Use above table to draw the diagram for $y=f\left(x\right)=x^2$Domain of function is $R$
and range is $[0,\infty )$.