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Graphing Logarithmic Functions Graph the function, not by plotting points, but by starting from the graphs in Figures 4 and 9. State the domain, range, and asymptote.$$y=\ln |x|$$

Domain: \((-\infty,0)\) \(\cup\) \((0,\infty)\) Range: \((-\infty,\infty)\), Vertical Asymptote at \(x=0\)

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Functions

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

Lectures

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In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Graphing Logarithmic Funct…

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Graph the function, not by…

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so remember that we know how to graft be the natural log function. And so so we also know how to graph when we have this absolute value on X. So this would be if this is X and this is why. And this is what our normal graph looks like. Remember at at X is equal to one. We have an X intercept and at X is equal to E. We have a value of one. Well, this if we have an absolute value of X, then then at negative one, this becomes positive one. And so this this behaves the same weight. But we still have. We still have our we still have. Our vertical Assen tote at X is equal to zero as X approaches zero the natural log function. So let's say we take a natural log of a very, very, very tiny number. Well, this would be negative. Infinity for what? Or approaching negativity. A very large negative number for why? And so so our graph is symmetrical. So it looks something like It's look something like this but also works the same way on the other side because of the absolute value on X but this looks like this looks like something like this. We have this asked meto and we go this way. So our graph looks like looks like this. And so for our domain here or our dummy, well X can be any value now except for zero. Because we have this vertical Assen toe at X equals zero and we can't take. We can't take natural logs. Zero There are domain. Here is from negative infinity to zero and and from zero to positive Infinity And our range here is still negative. Infinity, Our range is still negative. Infinity to positive infinity and finally are asking Tote, We said we said this was X is equal to zero. So these are solutions and this is our graph. This is our guy, remember? This is it may not look symmetrical in the sketch, but this is exactly symmetrical about the Y axis

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