Question

Draw the graph of `y= 2^({x})`, where `{*}` represents the fractional part function.

Answer 1

We have `y= f(x) = 2 ^({x})`
Now `{x}` is a periodic function with period 1.
Hence `f(x) = 2^({x})` is also periodic with period 1.
So we need to draw the graph for `x in [0, 1)` only. This part of the graph can be repeated to draw the graph in intervals `[n , n+1), n in Z`.
For `" "x in [0, 1), {x}=x`
`therefore" "y= 2^(x), x in [0, 1)`
So the graph of `y=f(x)` is as follows.