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  • - [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

對數函數圖解(例2)|代數2|可汗學院 (Graphing logarithmic functions (example 2) | Algebra 2 | Khan Academy)

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    林宜悉 發佈於 2021 年 01 月 14 日
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