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Sketch the graph of the function whose equation is given, using the first and second derivatives.$$y=f(x)=2 \log (4 x-5)$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 5

Logarithmic Functions

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Lectures

01:59

Sketch the graph of the fu…

01:58

00:29

Sketch the graph of $f$

02:02

00:53

Sketch the graph of each f…

coming up with a graph of these. There's a lot of different ways of doing. You know, you could make a table of values, use a graphing calculator. There's, Ah lot of different options on shifting up, down left right, uh, stretches compressions. But a good tool, I think, is to use a domain feature and that we can Onley log positive numbers. So what's in the parentheses must be greater than zero. The reason why this is a good strategy is you can easily subtract two and divide by five. I like negative two fists, but that's about negative 0.4 in case you prefer, that is, that's gonna help us identify a vertical ascent toe and that our domain is to the right because it's greater than eso. Maybe, you know, you just plot a point. Eso Let's say this is negative. One negative 10.4 would be about right here. Eso then from there, I would identify an X intercept. Well, the X intercept is when y equals zero eso. If I were to set this equation equal to zero changes, too. Exponential form will forward to the zero power equals one. It's equal to five X plus two. Well, then I can subtract two over. So that would make that negative one because five x so actually equal negative 1/5 which is, you know, negative point to its like right here and the X intercept. As far as everything else goes, it has the same behavior as a log where it's approaching the ass from tow. There's no other reflections either, Um, and then goes up into the right rather slowly. And that's the kind of graph I would create. Your teacher might want more points than what I've provided, though. Um, but I think this is pretty good right there.

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