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Sketch the graph of the function defined by the given equation.$$f(x)=3^{x}+2$$

$$y=3^{x}+2$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:00

Sketch the graph of the fu…

02:24

01:48

02:58

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02:51

03:00

03:13

Sketch the graph of functi…

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02:46

00:48

02:15

02:08

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00:36

So I have number 13. I'm here because otherwise it would just be We plug in random numbers into this and then hope we get out a good picture of their app. But since we already know what the parent function of three X plus two is, which is just three to the X, and we did that in number 13, we can use this graph here to kind of help us once we've made note of a couple of, um what sort of transformations that they have here. So what we're going to end up doing is the following. So first notice over here we're essentially just starting with like f of X. But then on the right side, so three to the X is f of X, but that we're adding to to this. So remember, any time we add on the outside is going to be a shift, and it's going to be just adding on the outside. Then it shifts. Oh, that many years would be shifting up to so we can take all of these points and then just shift everything up. Two units. So this one gets shifted up. Two units. Uh, this one gets shifted up. Two units. This one gets shifted up, two units just gets shifted up to and then this also gets shifted up to. So let me just go ahead and draw on the right side here first, and then we'd get really close. Now notice. All of these points are getting very close to zero. So now if we were to shift numbers, getting very close to zero up, that would be getting very close to two. So it's just gonna look a little bit like so you can see how it's just shifted up to us. And again, you could just plug in some arbitrary points. But at least doing it this way is a little bit easier. And actually, let me go ahead and fill this out wall. I'm here as well. So the only thing we're shifting or changing is the output. So the X value stay the same, so it'll be negative. 2101 and two, and then we're just going to add to to all these so 0.1 repeating becomes 2.1, repeating 0.3 becomes 2.3. Repeating one becomes 33 becomes 59 becomes 11 And then if you actually account for what we have there, you'll see that all those landed in the same place. So you don't necessarily need to make the church because you can just go ahead. And like I said, shift these up two units to get that sketch.

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