Name: Graphing square and cube root functions | Algebra 2 | Khan academy
Uploaded: 2020-03-27T17:41:13.000Z
Duration: 6 min 48 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

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

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

of y is equal to two times the square root

and so I encourage you to pause this video

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

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

so we already see what y equals the square root

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

let me put a negative x under the radical sign.

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,

So the y equals the square root of negative x

You've essentially flipped it over the y.

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

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

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

What will y equals two times the square root

Well, whatever y value we were getting before,

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

and so our curve is going to look something like,

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

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

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

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

All right, now let's work on this together

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

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

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

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Graphing square and cube root functions | Algebra 2 | Khan academy

essentially

figure

multiple

technique