Question

Draw the graph of the modulus function, defined by

$f:R\to R:f\left(x\right)=|x|=\{\begin{array}{c}x,\text{when}x\ge 0\\ -x,\text{when}x<0\end{array}$

Answer 1

We have

$\begin{array}{ccccccccc}x& -3& -2& -1& 0& 1& 2& 3& 4\\ f\left(x\right)=|x|& 3& 2& 1& 0& 1& 2& 3& 4\end{array}$

On a graph paper draw the horizontal line $X^{{}^{\prime }}OX$ as the x-axis and the vertical line $YO{Y}^{{}^{\prime }}$ as the y-axis.

Take the scale: 10 small divisions = 1 unit.

On this graph paper, plot the points A(-3, 3), B(-2, 2), C(-1, 1), O(0, 0), D(1, 1), E(2, 2), F(3, 3) and G(4, 4).

Join these points successively to obtain the graph lines ABCO and ODEFG, as shown below.