Graph each function. See Example 2. ƒ(x) = (1/3)^x

Question

Accepted Answer

Hello everybody I have today today. 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 F of X is equal to the fraction one divided by 15. And that fraction to the exponent X. Now, when looking at a question like this, I want to ask myself, what does my parent function look like? In our case, we have a fraction to an exponent X, but that fraction could be any number really? So when I think about that, I know that my parent function will be F of X is equal to A to the exponent X where in our case A is one divided by 15 but could be any number really. And now that I have my current function, I can ask myself to recall different rules and different things. I know about what the graph of A to the exponent X will look like. So that's exactly what I'll do now. So the first recall point I'll mention is that when we have the graph of A to the exponent X, we know three points will for sure be in our graph those points being negative one comma one divided by a, another point at zero, comma one in another point at one comma mm Now, like I mentioned before R A is one divided by 15. So our points will be negative one comma zero, comma one and one comma one divided by 15. And that'll be our first recall point. Now my second recall point here would be that if A is greater than one, our function F of X is increasing, it's an increasing function. But if zero is less than A is less than one, which basically just means if A is between zero and one, then our function will be a decreasing function. So F of X is decreasing in that scenario. And now, like we said before, we have an A of one divided by 15. So we'll have that zero is less than one divided by 15, which is less than one. Therefore, our afro bats is decreasing. Now, finally, my third point will have to do with, we'll deal with an, a horizontal Asymptote in our graph. So the graph of A to the exponent X has and A toads at Y equals zero, which is also the X axis. Now that I've made those three recall points. Now I have three points that will be part of our graph. I know that my function or my graph will be decreasing and I know of an ascent to in my graph. So I can go ahead and draw a general idea of what my graph would look like. That's exactly what we'll do. We'll draw a Y axis and an X axis and, and we know we'll have a Y intercept at zero comma one, we'll have a point at one comma one divided by 15, which is a very small Y of one comma one divided by 15. And finally, we'll have a point at negative one and comma 15, which is a much higher Y and we know that our function will be decreasing once we connect all those three points and then approach the X axis forever but never touch it as it is an Asymptote. So that will give us a general idea of what our graphs should look like here. So I hope that was helpful. And until next time.

Graph each function. See Example 2. ƒ(x) = (1/3)^x

Key Concepts

Exponential Functions

Graphing Techniques

Asymptotic Behavior

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