Placeholder Image

字幕表 動画を再生する

  • - [Instructor] We're told the graph of y is equal

  • to square root of x is shown below, fair enough.

  • Which of the following is the graph

  • of y is equal to two times the square root

  • of negative x minus one?

  • And they give us some choices here,

  • and so I encourage you to pause this video

  • and try to figure it out on your own

  • before we work through this together.

  • All right, now let's work through this together,

  • and the way that I'm going to do it

  • is I'm actually going to try to draw

  • what the graph of two times the square root

  • of negative x minus one should look like,

  • and then I'll just look at which of the choices

  • is closest to what I drew.

  • And the way that I'm going to do that

  • is I'm going to do it step by step,

  • so we already see what y equals the square root

  • of x looks like,

  • but let's say we just want to build up.

  • So let's say we want to now figure out

  • what is the graph of y is equal to the square root of?

  • Instead of an x under the radical sign,

  • let me put a negative x under the radical sign.

  • What would that do to it?

  • Well, whatever was happening at a certain value of x

  • will now happen at the negative of that value of x.

  • So the square root of x is not defined for negative numbers.

  • Now this one won't be defined for positive numbers.

  • And the behavior that you saw at x equals two,

  • you would now see at x equals negative two.

  • The behavior that you saw at x equals four,

  • you will now see at x equals negative four,

  • and so on and so forth.

  • So the y equals the square root of negative x

  • is going to look like this.

  • You've essentially flipped it over the y.

  • We have flipped it over the y axis.

  • All right, so we've done this part.

  • Now let's scale that.

  • Now let's multiply that by two.

  • So what would y is equal to two times the square root

  • of negative x look like?

  • Well, it would look like this red curve,

  • but at any given x value,

  • we're gonna get twice as high.

  • So at x equals negative four,

  • instead of getting to two,

  • we're now going to get to four.

  • At x equals negative nine,

  • instead of getting to three,

  • we are now going to get to six.

  • Now at x equals zero, we're still going to be at zero

  • 'cause two times zero is zero,

  • so it's going to look,

  • it's going to look like that.

  • Something like that,

  • so that's y equals two times the square root of negative x.

  • And then last but not least,

  • what will y,

  • let me do that in a different color.

  • What will y equals two times the square root

  • of negative x minus one look like?

  • Well, whatever y value we were getting before,

  • we're now just going to shift everything down by one.

  • So if we were at six before,

  • we're going to be at five now.

  • If we were at four before,

  • we're now going to be at three.

  • If we were at zero before,

  • we're now going to be at negative one,

  • and so our curve is going to look something like,

  • something like that.

  • So let's look for, let's see which choices match that.

  • So let me scroll down here,

  • and both C and D kind of look right, but notice,

  • right at zero, we want it to be at negative one,

  • so D is exactly what we had drawn.

  • And at nine, we're at five.

  • Or at negative nine, we're at five.

  • At negative four, we're at three,

  • and at zero, we're at negative one.

  • Exactly what we had drawn.

  • Let's do another example.

  • So here,

  • this is a similar question.

  • Now they graphed the cube root of x.

  • Y is equal to the cube root of x,

  • and then they say which of the following

  • is the graph of this business?

  • And they give us choices again,

  • so once again, pause this video and try to work it out

  • on your own before we do this together.

  • All right, now let's work on this together

  • and I'm gonna do the same technique.

  • I'm just gonna build it up piece by piece.

  • So this is already y is equal to the cube root of x.

  • So now let's build up on that.

  • Let's say we want to now have an x plus two

  • under the radical sign.

  • So let's graph y is equal to the cube root

  • of x plus two.

  • Well, what this does is it shifts the curve two to the left.

  • And we've gone over this in multiple videos before,

  • so we are now here,

  • and you could even try some values out

  • to verify that.

  • At x equals zero,

  • at x equals zero, or actually, let me put it this way.

  • At x equals negative two,

  • you're gonna kick the cube root of zero,

  • which is right over there.

  • So we have now shifted two to the left

  • to look something,

  • to look something like this,

  • and now, let's build up on that.

  • Let's multiply this times a negative,

  • so y is equal to the negative of the cube root

  • of x plus two.

  • What would that look like?

  • Well if you multiply your whole expression,

  • or in this case, the whole graph or the whole function

  • by a negative,

  • you're gonna flip it over the horizontal axis.

  • And so it is now going to look like this.

  • Whatever y value we're gonna get before

  • for a given x, you're now getting the opposite,

  • the negative of it.

  • So it's going to look,

  • it's going to look like that, something like that.

  • So that is y equal to the negative of the cube root

  • of x plus two.

  • And then last, but not least,

  • we are going to think about,

  • and I'm searching for an appropriate color.

  • I haven't used orange yet.

  • Y is equal to the negative of the cube root of x plus two,

  • and I'm going to add five.

  • So all that's going to do is take this last graph

  • and shift it up by five.

  • Whatever y value I was going to get before,

  • now I'm going to get five higher.

  • So five higher, let's see.

  • I was at zero here,

  • so I'm now going to be at five here.

  • So that's going to look,

  • it's going to look something,

  • something like,

  • something like that.

  • And I'm not drawing it perfectly,

  • but you get the general, the general idea,

  • now let's look at the choices.

  • And I think the key point to look at

  • is this point right over here,

  • that in our original graph, was at zero, zero.

  • Now it is going to be at negative two, comma, five.

  • So let's look for it,

  • and it also should be flipped.

  • So on the left hand side, we have the top part

  • and on the right hand side,

  • we have the part that goes lower.

  • So let's see.

  • So A, C, and B all have the left hand side

  • as the higher part

  • and then the right hand side being the lower part,

  • but we wanted this point to be at negative two, comma, five.

  • A doesn't have it there.

  • B doesn't have it there.

  • D we already said goes to the wrong direction.

  • It's increasing.

  • So let's see,

  • negative two, comma, five,

  • it's indeed what we expected.

  • This is pretty close to what we had drawn on our own,

  • so choice C.

- [Instructor] We're told the graph of y is equal

字幕と単語

動画の操作 ここで「動画」の調整と「字幕」の表示を設定することができます

A2 初級

平方根・立方根関数をグラフ化する|代数2|カーンアカデミー (Graphing square and cube root functions | Algebra 2 | Khan academy)

  • 2 0
    林宜悉 に公開 2021 年 01 月 14 日
動画の中の単語