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

Question

Provide a short answer to each question. Is ƒ(x)=1/x 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 nine divided by X is even or odd. And we are asked 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 and symmetric about the Y axis answer C odd and symmetric about the origin and D even and no symmetry. So again, our given function here is F of X is equal to nine divided by X. And now to first find whether this function is even or odd, we want to begin by finding F of negative X or in other words, substituting in negative X four X from our original function. So substituting in negative X, we have nine divided by negative X which rewriting we just have negative nine divided by X. And so here we see that also if we were to take the negative quantity of F of X, we would also get the same expression here of negative nine divided by X. So here we see F of negative X is equal to the negative quantity of F of X. And so because of this equivalent here we know that this is an odd function, this is an odd function. And since it is an odd function, it is symmetric about the origin. So here again, we have an odd function since F of negative X is equivalent to the negative quantity of F of X. And since it is an odd function, it is symmetric about the origin. So with these two pieces of information, we are left with answer choice C where again, we have an odd function that is symmetric about the origin. 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 an even or an odd function? What symmetry does its graph exhibit?

Key Concepts

Even and Odd Functions

Graphical Symmetry

Reciprocal Function

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