Question

Draw the graph of $y=\left[e^{\left[x\right]}\right]$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We will start with graph of $e^x$.

We will do the transformation $e^x\to \left[e^x\right]$.

If $x<0,0<e^x<1\Rightarrow \left[e^x\right]=0$

At $x=0,e^x=1$

At $x=ln2,e^x=2$

At $x=ln3,e^x=3$

So the graph of $\left[e^x\right]$ will look like

We will do the transformation $\left[e^x\right]\to \left[e^{\left[x\right]}\right]$

Now

For $x<0,\left[e^{\left[x\right]}\right]=0$

Between 0 and 1 $\left[e^{\left[x\right]}\right]=\left[e^0\right]=1$

$1\le x<2\Rightarrow \left[e^{\left[x\right]}\right]=\left[e^1\right]=2$

$2\le x<3\Rightarrow \left[e^{\left[x\right]}\right]=\left[e^2\right]=7$

So the graph will look like