Question

Which of the following can best represent the graph of $f\left(x\right)=e^{\left\{x\right\}}$?
[Note: $\left\{x\right\}$ denotes the fractional part of $x$]

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\left\{x\right\}$ is a periodic function with fundament period $1$. So, we need to draw graph from $[0,1)$ and it will get repeated after that.
$\left\{x\right\}$ is an increasing function in $[0,1)\Rightarrow e^{\left\{x\right\}}$ is also increasing in $[0,1)$
at $x=0,e^{\left\{x\right\}}=1$ and
at $x\to 1,e^{\left\{x\right\}}\approx e$

So, the range of $e^{\left\{x\right\}}$ is $[1,e)$
The correct graph is,