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

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

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Harvey Mudd College

Baylor University

Idaho State University

Lectures

02:58

Sketch the graph of the fu…

02:24

01:48

01:55

02:00

02:25

03:00

02:15

02:08

02:46

00:25

03:01

Sketch the graph of functi…

But if we want to sketch this crap three X minus two minus three. What we can do instead of just arbitrary plugging in some numbers, we can use its parent function, which we actually sketched in number 13 here. And we can use that along with some transformation to kind of help us out a little bit. So, um, notice here on the left, it's like we start with F a bex and then on the right side, this is going to become f of X minus two because we have three to the X and the X essentially just got replaced by X my students. And then we just subtracted three on the outside. So remember this Xmas, too, on the inside is selling a shift, um, two units and we're going to go to the right because on the inside, it's always the opposite of what I normally want to say. It is, uh, and then on the outside, well, that's going to be vertical changes. It would be up or down since we're adding, so it's still shift, but now it's going to be down three units so we can just come over here and first make our new chart. So the X values were just gonna add to to all of them would become zero, 123 and four And then for the outputs, we're just going to subtract three from all of them. So this is going to become negative. 2.8, repeating, um, 0.3 repeating is going to become negative 2.6 repeating, um, one is going to become negative, too. Three is going to become zero, and then nine is going to become seven. And then we can just go in and plant these or again, you can just go ahead and move all of these, um, to to the right and then three down. So 12123 12123 12123 Um, another one too. 12 three. And then the next one would be kind of there. All right. And then we can just go ahead and connect all of them, so it looks something kind of like So now one thing to notice is so for our original function, we're getting very close to zero on the left side. So if I shifted that down three now that should get very close. Two negative three instead. So that would be our Kurt. Then again, like I said, you could just plug in a bunch of different points. Um, but it's not very interesting to do it that way because you never really know how good your sketch actually is. But if you know the parent function, doing these transformation makes it a lot easier.

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