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Sketch the graph of the function defined by the given equation.$$f(x)=5\left(2^{-x}\right)$$

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

Harvey Mudd College

Baylor University

Lectures

02:17

Sketch the graph of $f$

00:40

00:36

Sketch the graph of each f…

01:15

02:10

02:12

02:27

Sketch the graph of the fu…

01:23

04:09

01:30

Sketch the graph of functi…

So if we want to sketch this graph here, normally, any time we have something of the form of a ties be to something or some power the moment you could just go ahead and use these values here, and it should normally give you a pretty decent sketch of the graphs. Let's just go out and plug these in that we can kind of go from there. So if we plug in zero to start, it would be five times two to the zero, which is just going to be 512345 if I go ahead and plug in, one would be five times two to the negative first, which the same thing as five halfs for 2.5. So that would be somewhere around, like here. Then we go ahead and plug into so five times, two to the negative, too. 75/2 squared, and then that would just be five or four or 1.25 So that is maybe around, like, here or so. All right. Uh, then if we plug in negative one, this is going to end up giving us five times two. So the negatives cancel. So it's just five times to it would be 10. So this is 56789 10. And then if we were to plug in negative to, it was just kind of go off the page. So I'm just gonna go ahead and leave it here like this. So now, after this point, you could plug in a couple more values to the right if you wanted. But which will end up seeing is that the values are just going to keep getting closer and closer to the X axis on the right side. And we know anytime we have an exponential in this forum on the left or right, it gets closer and closer to the X axis. So it's just going to look something kind of lake. This other than that would be a harder sketch of this ground.

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