Question

The graph of $f\left(x\right)=e^{x^2}$, where $e>1$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The graph of $e^x$ is

The graph of $e^x$ is decreases as $x$ decreases and when $x<0,$ $e^x$ converted into $\frac{1}{e^x}$ due to negative $x$.
But in case of $x^2$ it's always positive and minimum at $x=0.$
So, the graph of $e^{x^2}$ when $x<0$ is same as the graph of $e^{x^2}$ when $x>0.$
Therefore, the graph is symmetric about the $y-$ axis and the minimum value of $e^{x^2}$ is $1$ at $x=0.$

Now, the nature of $e^{x^2}$ is same as $e^x$ because $e>1,$ the only difference is that the inceasing rate is more than the graph $e^x.$
So, the required graph is