Question

Draw the graph of each of the following constant functions:

(i) $f\left(x\right)=2$ for all $xϵR$

(ii) $f\left(x\right)=0$ for all $xϵR$

(iii) $f\left(x\right)=-2$ for all $xϵR$

Answer 1

(i) Let $f\left(x\right)=2$ for all $xϵR$

Then, $\text{dom (f)}=R$ and range (f) = {2}

We may prepare the table given below.

$\begin{array}{ccccccc}x& -2& -1& 0& 1& 2& 3\\ f\left(x\right)=2& 2& 2& 2& 2& 2& 2\end{array}$

On a graph paper, we draw $X^{{}^{\prime }}OX$ and $YO{Y}^{{}^{\prime }}$ 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) and F(3, 2). Join A, B, C, D, E and F successively to obtain the required graph line ABCDEF, whose equation is y = 2.