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Sketch the graph of the function whose equation is given, using the first and second derivatives.$$y=f(x)=3 \log (2 x+3)$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 5

Logarithmic Functions

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

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Sketch the graph of the fu…

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Sketch the graph of $f$.

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eso There's lots of different ways to come up with a graph. You could make a table values. Um, you could use a graphing calculator. I don't know if if we're supposed to in this, um, but what I would do is just start with identifying the domain and in the in this problem since we're logging, we can Onley log positive numbers. So if I were to ask you to find the kind of numbers we can plug in for X, we would have to have Onley greater than zero. So subtract one and divide by two. Uh, this is identifying the vertical Assam tote of our graph. So let's say this was negative one. The vertical aspect. It would be halfway over here, Um, and we can on lee be on the right side of that vertical ascent. Oh, because it's greater than so. Maybe another step to take would be to identify the X intercept on That's when why equals zero. So if we set up the equation that way is is a log based three of two X plus one equals zero. Well, then we can change this toe exponential form. So three to the zero power is one is equal to two X plus one. Subtract one over, so x one equals zero. So the origin is actually our X intercept. Um, and then there's no other reflections in any way, shape or form. So maybe just make your graph does not look like it's getting closer and closer, you know, in this way and this way, and you might want to pick out a few more points. But this is essentially your graph that we want in this problem, so

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