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$49-52$ Graphing Logarithmic Functions Sketch the graph ofthe function by plotting points.$$g(x)=\log _{4} x$$

The curve and data table of the function $f(x)=\log _{4} x$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Missouri State University

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Harvey Mudd College

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Lectures

02:34

Graphing Logarithmic Funct…

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Sketch the graph of the fu…

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In Exercises $43-46,$ sket…

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In Exercises $47-52$ , des…

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In Exercises $47-52$ , fin…

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In Exercises 51-56, sketch…

So if you want to sketch this function well, the first thing we can do is convert this this log rhythmic equation into an exponential equation. So we can have. We can say our base for race to wise is this equal to X. And so now if we have, if we have X is equal to, let's say, for example, one then are wise equal to zero. If X is equal to four, then are wise equal to one. And let's say X is equal to Let's say X is equal to 16. Well, then why is equal to two? And so if we were to graft this, let's say we're graphing this year. This is X, and this is our Y axis. So we have X is equal to one. Why's X is equal to four? So this is one. This is, Let's say, for example, this is four, therefore, is a little bit further down a little bit further down, or and this is all the way at 16. Well, when X is equal to one, y is equal to zero. When X is equal to four. Why is equal to one and when X is equal to 16. Why is equal to two? So let's look at the the end values well when X approaches when X approaches. Zero. Remember, we could never have some value to an export of that equal zero. But this number can get it increasingly closer to zero as y approaches negative infinity. And so so our graph when x approaches. Zero This why approaches negative infinity And when X gets really, really, really large, so would our Why value. So let's let's crafty. So when we have X is equal to one wise equal to zero when X is equal to four wise equal to one and when X is equal to 16 why is equal to two? But this graph has a has a vertical ass in tow. We haven't asked until here and our graph goes, paragraph goes, How important two and family is there a graph looks something like this. So it'll keep continuing up till infinity but are slow. Gets a little bit little evens off. But it will still go to infinity as X approaches infinity and why will go to infinity

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