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$79-84$ Graphing Logarithmic Functions Draw the graph ofthe function in a suitable viewing rectangle, and use it to find thedomain, the asymptotes, and the local maximum and minimumvalues.$$y=x \log _{10}(x+10)$$

See explanation for graph.Domain: $(0, \infty)$Asymptotes: $x=0, y=\frac{1}{e} \approx .368$Local maximum: $\left(e, \frac{1}{e}\right) \approx(2.718, .368)$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Campbell University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

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now over here in description. We just have to draw the graph for the function that sees. Why is it will toe eggs law be Spain Eggs plus pain. Fine. You can just take the helpful for graphing utility on, uh, on the graphing calculator. Just enter this given function using the Y equal to keep with a fine. Now, once you enter the function, do not forget to set a proper viewing Recanted or you can see the green window over the body graphing screen over it. Alright, So talking about the wing window just set a proper I mean proper eggs, axes and the proper by access. So you can just say living rectangle as minus two to in bye minus 4 to 10. So once you say the proper win window and the and once you enter their function will take a graph similar to the one that I've shown here on the screen. So this blue curve over here representing graph for viable toe eighth love based in eggs plus being what? No, we've got the code or the craft in front off us now. Once you return minded crab, we have to find out the same toads, the domain dreams as well as the maximum and minimum values. So now what is meant by the term I seemed tools. So simply, I seem to it is just a line that the curve approaches but never touches. So we're here. The line, as you can see over here, X is approaching towards minus m. Fine. Just look over here. It is approaching towards minus Tendo. So simply the line X is equal to minus 10 is the vertical. I seem to it for a given function. Now, talking about the domain over here, the domain will range from minus tend to infinity. Well, Onda talking about the maximum and the minimum values. So to find out the local minimum, we can see that the minimum value is occurring. Some water over here, right? So to find the local minimum or the minimum value, just zoom in on the trees along the gravity person. Right? So once you do the tracing and all, you'll find that the minimum value is a cream at Since the minimum value is a thing that way, where there are what are the coordinates? The minimum value is minus 3.6 TEU. Annika occurs when Aces goto minus 5.87 Right. So the minimum value for the corn it will be minus 5.87 coma minus three point 60. So this is how you will determine the graph and the falling features from the craft.

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