Draw the graph of each of the following constant functions: (i) f(x)=2 for all `x""inR` (ii) f(x)=0 for all `x""inR` (iii)f(x)=-2 for all `x""inR`

Explanation

(i) Let f(x) =2 for all `x""inR`.
Then, dom (f) =R and range `(f)={2}`.
We may prepare the table given below.

On a graph paper, we draw X' OX and YOY' as the x-axis and the y-axis respectively.
We take the scale: 10 small divisions =1 unit.
On this graph paper, we plot the points `A(-2,2),B(-1,2),C(0 ,2),D(1,2),E(2,2)andF(3,2)` Join A, B, C, D, E, and F successively to obtian the required graph line ABCDEF, whose equation is y=2.

(ii) Let f(x)=0 for all `x""inR`. Then, dom (f)=R and range `(f)={0}`.
Now, we have:

On a graph paper, we draw the horizontal line X' OX as the x-aixs and the vertical line YOY' as the y-axis.
We take the scale: 10 small divisions = 1 unit.
Now, on this graph paper, we plot the points A(-2,0), B(-1,0), O(0,0), C(1,0) and D(2,0) and join them successively to get the graph line ABOCD, whose equation is y=0.

(iii) Let f(x)=-2 for all `x""ininR`. Then,
dom (f) =R and range (f)=-2.
Now, we have:

On a graph paper, we draw the horzontal line X' OX as the x-axis and the vertical line YOY' as the y-axis.
We take the scale: 10 small divisions =1 unit.
On this graph paper, we plot the points A(-2,2), B(-1,2), C(0,-2), D(1,-2), E(2,-2) and F(3,-2) and join these points successively to get required graph line ABCDE, as shown belw. Its equation is y=-2.