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

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

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 we know how to find the graph of the natural law function. But here we'll find whereas to find the absolute value of it, well, we know that our graph looks like So let's say this in our accents are why is our X and start y axis? We know that at X is equal to 21 This this graph is equal to zero does their X intercept. And so we know we also know that at X is equal to e are y is equal to are y is equal to 21 Let's say this is one X is equal to one. And so So this is our point here. But instead of as X approaches zero instead of why going from negative infinity, we have to take the absolute value of this. So this means that this means that our graph goes from from positive infinity positive infinity 2 to 1 and then goes back this way goes back this way. And so this is This is our absolute value of the of the natural log function. We don't have any any negative. Why values So So this is what our graph looks like and So we noticed here that we still have this vertical Assen towed at at X is equal to zero. So let's find our domain range. So domain is from is from zero to infinity and our range is from negative infinity to positive infinity and are asking to remember we said this was at this was at X is equal to zero. And so these are our solutions and this is this is our graph.

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