A way to test whether a function is odd/even using calculator

Question

Could you show me an easy and fast way to test whether a function is odd or even using the calculator ?

I've only came across the graphing way and another algebraic way and I'm afraid to make a silly mistake while doing them.

Answer 1

Does the definition count?

Odd functions are functions such that $$f(-x) = -f(x)$$ and even functions are such that $$f(-x) = f(x)$$ for all $x$ in the domain of $f$.

Graphically, odd functions are symmetric about the origin and even functions are symmetric about the $y$-axis.

Answer 2

Try the following: Pick a random value $x$ such that $x$ and $-x$ are in your domain, which I assume here is all of $\mathbb{R}$. Use your calculator to evaluate $f(x)$ and $f(-x)$.

If $f(x)=f(-x)$ your function is even. If $f(x)=-f(-x)$ your function is odd. If neither of these relations hold, then neither is true.

WARNING: Just because one of these relations holds for a specific choice of $x$, does not mean it holds for all $x$. This is a good way of checking your work, but the algebraic way is generally the only full way to check this.

Answer 3

Great question.

I myself had some difficulty understanding the difference between even and odd functions. I found this PurpleMath article on even/odd functions pivotal in my understanding of them.

For finding even/odd function on your calculator, I just used the function manager of a TI-84.

The function shown is from the first example on that PurpleMath page I linked, -3x^2+4.

I then go to the table using 2nd/GRAPH, and input a value of x and -x as independent values.

As you can see, f(x) and f(-x) are both -296, thus the function is even, as the PurpleMath article corroborates.

You may be wondering: "Well, what about odd and neither? How do I determine those?" As stated in the PurpleMath article, in an odd function f(-x) will be the exact opposite of what we started with, or f(x). In a function that's neither even nor odd, f(-x) will not be the same or the opposite of f(x).