Provide a short answer to each question. Is ƒ(x)=1/x^2 an even or...

Question

Provide a short answer to each question. Is ƒ(x)=1/x^2 an even or an odd function? What symmetry does its graph exhibit?

Accepted Answer

Hey, everyone here we are asked to identify whether the function F of X is equal to three divided by X rays to the fourth power is even or odd. And we need to tell something about its symmetry. Here, we have four answer choice options, answer a odd and symmetric about the X axis. Answer B even symmetric about the Y axis, answer C odd no symmetry and answer D even and symmetric about the origin. So looking at our given function against again, we have F of X is equal to three divided by X rays to the fourth power. And so to test whether this function is even or odd, we need to substitute in negative X four X. Or in other words, we need to find F of negative X. And so substituting in negative X, we get the expression three divided by the quantity of negative X raise to the fourth power. Now, if we raise negative X to the fourth power, we see that this term, this X term is going to be positive. So this expression is actually just three divided by X to the fourth power. And so with this, we see that F of negative X is the same as or equivalent to F of X. And this tells us this statement tells us that our original function F of X is an even function. So it is an even function. And it, since it is even, it tells us that this function is symmetric about the Y axis. So again, we have an even function because F of negative X is equal to F of X. And because it is even we know that the function is symmetric about the Y axis. So with these pieces of information, we are left with answer choice B where again, we have an even function that is symmetric about the Y axis. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Provide a short answer to each question. Is ƒ(x)=1/x^2 an even or an odd function? What symmetry does its graph exhibit?

Key Concepts

Even and Odd Functions

Graphical Symmetry

Reciprocal Functions

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