Graph each function. See Example 2. ƒ(x) = 4^-x

Question

Accepted Answer

Hello, everybody. I have everything right today. So we're going to be looking at this math question that states plot the given function on the rectangular coordinate system where our function is of X is equal to nine to the exponent negative XX. Now we looking at a question like this where I see they're asking me to plot a function. The first thing I wanna do is test multiple points. So I like to make a tea chart sorts where I have X values on the left and Y values on the right. And I see that we're gonna have the XS as exponents here. So I know that my values are gonna go very high very quickly. So I'll just stick with negative two, negative 101 and two. And now I have to plug this into our function. So if we plug in negative two to our exponent, we'll have nine to the exponent negative negative two, which means we'll have nine to the positive two to the exponent positive two, which is equal to 81. So that we are Y or an X of negative two. If we have an X of negative one we'll have nine to the exponent negative negative one, which is the same as saying nine to the exponent positive one, which is nine. So that'll be a Y, if we haven't explained the zero, we'll have nine to the zero, which is just one. So that'll be our point there. If we have an exponent of X of one, we'll have nine to the exponent negative one which is equal to one divided by nine to the first power, which is equal to one divided by nine. And finally, we have an exponent of two, we'll have nine to the exponent negative two, which is equal to one divided by nine to the exponent positive two, which is equal to one over 81. So the next thing I wanna do is I see that I have an exponential equation here. And I'm going to recall that if our function, we have a function of alphabets, let's say we have it in the form of A B to the exponent K X. And outside of that plus C, in our case, we would, we just have a B to the K X K being negative one and X being R X, if we have a function in that formula, then we'll have a horizontal as some toads at Y equals C. So for our case C equals zero, since we're not adding anything, there are four are horizontal Asymptote is Y equals zero. So with that information, we can now plot a graph. So we have some different points and we know where there's gonna be a horizontal acid tilt. So now we just have to plot it. So we'll draw a Y axis and an X axis and we know that if we have an uh our, our Y intercept is going to be at zero comma one. So at a Y one, we're going to have a point that'll be our zero comma one. Then we tested a point at negative up negative one and X up positive one and a point at X up negative two N X of positive two. Now, as we said, we know that the X axis or Y equal zero is going to be our horizontal as tode. So at X of one, we know we're going to have a point of around one divided by nine. And then this would just continue to go low, low, low, almost touching the X axis forever, but never actually reaching it at a, at an X of negative one. We said we would get a Y of positive nine. So we'll have a point there. And then we said an X of negative two R Y would be 81 which means this will shoot upwards very quickly. So that'll kind of be the shape of our graph. It's almost like an L just more open where we have a horizontal asom tilt at X axis at the X axis. A point at one comma one divided by nine, a one intercept of zero comma one and another point at negative one comma positive nine. So that is what our graph will look like. So I hope that was helpful. And until next time.

Graph each function. See Example 2. ƒ(x) = 4^-x

Key Concepts

Exponential Functions

Graphing Techniques

Asymptotes

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