 ## 字幕表 動画を再生する

• - [Instructor] This is a screenshot

• from an exercise on Khan Academy,

• and it says the intergraphic, the interactive graph below

• contains the graph of y is equal

• to log base two of x as a dashed curve,

• and you can see it down there as a dashed curve,

• with the points one comma zero

• and two comma one highlighted.

• Adjust the movable graph to draw y is equal

• to four times log base two of x plus six minus seven.

• And so if you happen to have this exercise in front of you

• I encourage you to do that.

• Or if you're just thinking about in your head,

• think about how you would approach this.

• And I'll give you a hint, to go from our original

• y is equal to log base two of x to all of this,

• it's really going to be a series of transformations.

• And on this tool right over here,

• what we can do is we can move this vertical asymptote around

• so that's one thing we can move,

• and then we can also move two of these points.

• So where we're starting is right,

• we are starting right over there.

• And so let's see, and that was just the graph

• of y is equal to log base two of x.

• So let's just do these transformations one at a time.

• So the first thing I am going to do,

• instead of just doing log base two of x,

• let's do log base two of x plus six.

• So if you replace your x with an x plus six,

• what is it going to do?

• Well it's going to shift everything six to the left,

• and if that doesn't make intuitive sense to you,

• I encourage you to watch some

• of the introductory videos on shifting transformations.

• So everything is going to shift six to the left.

• So this vertical asymptote is going to shift six to the left

• it's gonna be, instead of being at x equals zero,

• it's going to go all the way to x equals negative six.

• This point right over here, which was at one comma zero,

• it's going to go six to the left,

• one, two, three, four, five, six.

• And this point, which as at two comma one,

• is gonna go six to the left,

• one, two, three, four, five, and six.

• So so far what we have graphed

• is log base two of x plus six.

• So the next thing we might wanna do is

• what is four time log base two of x plus six.

• And I want you to think about it is

• whatever y-value we were getting before,

• we're now going to get four times that.

• So when x is equal to negative five,

• we're getting a y-value of zero,

• but four times zero is still zero,

• so that point will stay the same.

• But when x is equal to negative four,

• we're getting a y-value of one,

• but now that's going to be four times higher,

• 'cause we're putting that four out front,

• so instead of being at four,

• instead of being at one it's going to be at four.

• So this right over here is the graph

• of y is equal to log base two of x plus six.

• And then the last thing we have to consider

• is well we're gonna take all of that

• and then we're going to subtract seven

• to get to our target graph.

• So whatever points we are here,

• we are now going to subtract seven.

• So this is at y equals zero,

• but now we're going to subtract seven, so we're going to

• go down one, two, three, four, five, six, seven,

• I went off the screen a little bit, but let me see

• if I can scroll down a little bit so that you can see that,

• almost, there you go, now you can see.

• I moved this down from zero to negative seven,

• and then this one I have to move down seven,

• one, two, three, four, five, six, and seven,

• and we're done, there you have it.

• That is the graph of y is equal to four times log base two

• of x plus six minus seven, and we are done.

- [Instructor] This is a screenshot

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A2 初級

# 対数関数をグラフ化する（例2）｜代数学2｜カーンアカデミー (Graphing logarithmic functions (example 2) | Algebra 2 | Khan Academy)

• 3 0
林宜悉 に公開 2021 年 01 月 14 日