Draw the graph of the exponential funcation.
(i) ` f(x) = 2^(x)` (ii) ` f(x) = (1/3)^(x)`

Explanation

(i) ` f(x) =2^(x)`
Some of the points on the graph are
(0,1) , (1,2) , (2,4),(3,8) , ` ( -1, 1/2), (-2,1/4), (-3,1/8) ` etc.
And so the graph takes the form, shown in the adjoining figure.
It may be observed here that the given funcation is strictly increasing. Also, as the value of x decrease, the corresponding value of the funcation descreases, and therefore, on the left-hand side of the y -axis , the curve comes closer and closer to the x-axis.
(ii) Let ` f(x) = (1/3) ^(3) = 1/(3^(x))`
some of the points on the graph are ( -2,9)
`(-1,3) , (0,1) (1,1/3), (2,1/9)` , etc.
Joining these, points, we obtain the graph as shown. if follows the graph the given funcation is strictly decreasing .
On the RHS of the y-axis. the curve comes closer and closer to the x-axis.