yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Even and odd functions: Tables | Transformations of functions | Algebra 2 | Khan Academy


3m read
·Nov 10, 2024

We're told this table defines function f. All right, for every x, they give us the corresponding f of x according to the table. Is f even, odd, or neither? So pause this video and see if you can figure that out on your own.

All right, now let's work on this together. So let's just remind ourselves the definition of even and odd. One definition that we can think of is that f of x is equal to f of negative x; then we are dealing with an even function.

If f of x is equal to the negative of f of negative x, or another way of saying that, if f of negative x, if f of negative x, instead of it being equal to f of x, it's equal to negative f of x, these last two are equivalent. Then in these situations, we are dealing with an odd function. If neither of these are true, then we're dealing with neither.

So what about what's going on over here? So let's see, f of negative seven is equal to negative one. What about f of the negative of negative seven? Well, that would be f of seven, and we see f of 7 here is also equal to negative 1. So at least in that case, in that case, if we think of x as 7, f of x is equal to f of negative x, so it works for that.

It also works for negative three and three. f of three is equal to f of negative three; they're both equal to two, and you can see, and you can kind of visualize in your head that we have this symmetry around the y-axis. So this looks like an even function. So I will circle that.

Let's do another example. So here, once again, the table defines function f. It's a different function. Is this function even, odd, or neither? So pause this video and try to think about it.

All right, so let's just try a few examples. So here we have f of five is equal to two. f of five is equal to two. What is f of negative 5? f of negative 5, not only is it not equal to 2, it would have to be equal to 2 if this was an even function, and it would be equal to negative 2 if this was an odd function, but it's neither.

So we very clearly see, just looking at that data point, that this can neither be even nor odd. So I would say neither, or neither, right over here.

Let's do one more example. Once again, the table defines function f. According to the table, is it even, odd, or neither? Pause the video again, try to answer it.

All right, so actually, let's just start over here. So we have f of 4 is equal to negative 8. What is f of negative 4? And the whole idea here is I want to say, okay, if f of x is equal to something, what is f of negative x? Well, they luckily give us f of negative 4; it is equal to 8.

So it looks like it's not equal to f of x; it's equal to the negative of f of x. This is equal to the negative of f of 4. So on that data point alone, at least that data point satisfies it being odd; it's equal to the negative of f of x.

But now let's try the other points just to make sure. So f of one is equal to five. What is f of negative one? Well, it is equal to negative five. Once again, f of negative x is equal to the negative of f of x, so that checks out.

Then f of 0, well, f of 0 is of course equal to 0. But of course, if you say what is the negative of f of, if you say what f of negative of zero, well that's still f of zero. And then if you were to take the negative of zero, that's still zero.

So you could view this, this is consistent still with being odd. This, you could view as the negative of f of negative zero, which of course is still going to be zero. So this one is looking pretty good that it is odd.

More Articles

View All
Why the UK Election Results are the Worst in History.
Hello Internet. The UK had an election we need to talk about because after the debates finished, the people voted and the ballots tallied the results were this: But parliament ended up looking like this: which isn’t, exactly, representative. And by not e…
A Napa Valley Nature Walk | National Geographic
Hi! I’m Ashley Kalina, and I’m here in beautiful Napa Valley to talk to you about National Get Outdoors Day. I’m here with National Geographic and our friends at Nature Valley. We’re here to experience the beautiful outdoors. Now, I’m not the expert here…
Angular momentum of an extended object | Physics | Khan Academy
[Voiceover] So we saw in previous videos that a ball of mass m rotating in a circle of radius r at a speed v has what we call angular momentum, and the symbol we use for angular momentum is a capital L. The amount of angular momentum that it would have wo…
Interwoven | Vocabulary | Khan Academy
I’ve got a twisted tale to tell you in this video, wordsmiths, because the word I want to talk about is interwoven. Interwoven, it’s an adjective, and it means twisted or joined together. It has a literal meaning, like two fibers woven into the same carpe…
Canyon Catharsis | Badlands, Texas
I’ve been through this canyon over 750 times. This is a place where you can hear the voice of God bouncing off these walls in the wind. There’s no roar, no freeways, no trial. Silence. For years, I was a river guide here with Tony. I remember when Tony f…
How to take AI from vision to practice. Part 1
Welcome everyone! We are so excited for you to be here, uh, to join this amazing conversation. My name is Danielle Sullivan. I’m the senior regional manager of the Northeast Partner District Partnerships at Khan Academy, and I’m really thrilled, uh, that …