Name: Graphing logarithmic functions (example 1) | Algebra 2 | Khan Academy
Uploaded: 2020-03-27T17:35:52.000Z
Duration: 5 min 27 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 are told the graph of y is equal

To-infinitive

to two log base two of negative x minus three.

The way to think about it is that this second equation

that we wanna graph is really based on this first equation

So I encourage you to take some graph paper out

Now the difference between what I just wrote in purple

and where we wanna go is in the first case

we don't multiply anything times our log base two of x,

while in our end goal we multiply by two.

In our first situation, we just have log base two of x

So what we could do is try to keep changing this equation

So maybe the first thing we might want to do

is let's replace our x with a negative x.

at a given x-value, so for example when x equals four

So log base two of the negative of negative four,

but now that's going to happen at negative one

'cause you take the negative of negative one,

And so similarly when you had at x equals eight

you got to three, now that's going to happen

at x equals negative eight we are going to be at three.

And so the graph is going to look something like

hey let's replace this x with an x plus three,

in terms of what we're taking the log of,

So now let's think about y is equal to log base two of,

and actually I should put parentheses in that previous one

so log base two of not just the negative of x,

but we're going to replace x with x plus three.

Now what happens if you replace x with an x plus three?

Or you could even view x plus three as the same thing

that when you replace x with an x plus three

that will shift your entire graph three to the left.

So this shifts, shifts three to the left.

Well when the point where we used to hit zero

are now going to happen three to the left of that.

So we used to hit it at x equals negative one,

now it's going to happen at x equals negative four.

instead of happening at x equals negative four,

is now going to happen three to the left of that

And the point at which the graph goes down to infinity,

as x approaches three to the left of that,

so I could draw a little dotted line right over here

So our graph's gonna look something, something like this,

so it's not perfectly drawn but we're awfully close.

Now to get from where we are to our goal,

we just have to multiply the right hand side by two.

So now let's graph y, not two, let's graph y is equal

to two log base two of negative of x plus three,

which is the exact same goal as we had before,

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Graphing logarithmic functions (example 1) | Algebra 2 | Khan Academy

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