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• - [Instructor] 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,

• if f of x is equal to f of negative x,

• then we're dealing with an even function.

• And 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.

• And 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 seven here is also equal to negative one.

• So at least in that case and that case,

• if we think of x as seven,

• 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 symmetry around the y-axis.

• And so this looks like an even function.

• So I will circle that in.

• Let's do another example.

• So here, once again, the table defines function f.

• It's a different function f.

• 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 five?

• F of negative five.

• Not only is it not equal to two,

• it would have to be equal to two

• if this was an even function.

• And it would be equal to negative two

• 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.

• All right, so actually let's just start over here.

• So we have f of four is equal to negative eight.

• What is f of negative four?

• And the whole idea here is I wanna say,

• okay, if f of x is equal to something,

• what is f of negative x?

• Well, they luckily give us f of negative four.

• It is equal to eight.

• 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 four.

• 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.

• And then f of zero,

• well, f of zero is of course equal to zero.

• 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.

- [Instructor] We're told this table defines function f.

A2 初級

# 偶函數和奇函數。代數2｜代數2｜Khan Academy (Even and odd functions: Tables | Transformations of functions | Algebra 2 | Khan Academy)

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林宜悉 發佈於 2021 年 01 月 14 日