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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.$$y=1+\ln (-x)$$

domain: \((-\infty,0)\) 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

Baylor University

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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remember that we already know how to you grab the natural log of Negative X because if we convert this to exponential form, what we would have e to the wise equal to negative x you to the y is equal to negative X. And so this gives us negativity to why is equal to X eso. So now if we have we have we realized that that X has to be always negative because each otherwise always possible than our graph looks something like something like this. We still have our wrote a glass into and our graph looks like this. So So now we want to add one to this. So we know that this this point occurs here when, when y is equal to zero, this is this is X is equal to negative one. So this is negative one. But now we want to add this to one. So we wanna increase this graph upward by one. So at that now negative one we have, we have y is equal to one. So if we wanted to draw this again, well then then at X is equal to negative one. This is also equal to 21 So we have a point here. And so in our graph shifted upward looks something like shifted upward looks something like this. And so this is Remember, our X axis and our waxes They're X axis is there y axis. And so now we're gonna find the domain here. Our domain is he said, Well, I explained so this would be from negative infinity to zero. Our range would still be from from negative infinity to positive acidity and rs in total still occurs at X is equal to zero. So these are our solutions and this is a sketch of our graph.

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