Curve sketching for the function f(x) a) What is the domain of f(x). b) Is the function odd, even or neither odd nor even? c) What are the zeros of f(x)? d) What are the poles of f(x)? e) Calculate the first three derivatives of f(x). f) Determine the turning points of f(x). g) Determine the inflection points of f(x). h) What is the limit of f(x) for x→ ±00?

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What is Graph of a Function:

Graph of a function is the graphical representation. Since, the graph is visible to us, it helps us to understand the function in an efficient way. Many analytical natures can be understood from the graph. There are some certain things which are necessary to draw a graph. If those points are known to use, one can draw the graph of a given function. 

Given:

Given function is, $f\left(x\right)=\frac{x^2-1}{e^x}$.

To Determine:

We determine the domain and zeros of the function. We also determine whether the function is even or odd.