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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

02:25

Sketch the graph of the fu…

02:24

01:48

02:58

01:55

02:51

03:00

03:13

Sketch the graph of functi…

03:01

02:46

00:48

02:15

02:08

00:24

00:36

so you might notice. Here I have number 13 on the board. Still, And the reason why I have that is because we can use that to kind of bootstrap us into this one. Um, because otherwise it's just We plug in a bunch of different numbers and hope we get a good graph out. But since we already have a good graph from number 13, we can use some transformations to kind of help us out. Because notice what we did here was on the left side. If we started with F Becks on the right, and this is essentially like, we replaced X with X plus two. And so we know when we do a transformation like this, this is going to be a shift. And since we're adding on the inside, it will be to the left. So we shift two units left. So that means these X values are going to be just like we subtract four from them, so negative to becomes negative for negative one becomes negative, 30 becomes negative to one, becomes negative one, and to become zero and then all the X value or the output values are going to stay the same. So still be 0.1. Repeating 0.3, repeating one, three and nine or again, you can just think, Oh, I'm taking these and then shifting them to love. So, like this first one just shifted. Two years to look this 12 units that left this 12 units that left this 12 units have left, um, and then this 12 units to the left. So it looks something kind of like this and again, Like I was saying, you could just go ahead and plug all of these values and, um and then just hope you kind of get like, a nice sketch of it. But since we already know what a nice sketch of it is using its parent function just three to the X. Um, it's normally a good idea, just kind of go ahead and use that to kind of help us out

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