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

Question

Accepted Answer

Hello everybody. And I today that 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 15 to the exponent X. Now when looking at a question like this, I see that we have a number to exponent X. So I know that there's going to be a parent function here or a general form form of our function. So in our case that parent function will be F of X is equal to A, to the exponent X where R A is equal to 15. So that A could be any number realistically. But I'm just pointing out that for our case, it's a 15. So now that I know that what the parent function is A to the exponent X, I can recall different rules and different things that I know about what the graph of A to the exponent X would look like. And my first recall point will deal with three points that I know will for sure be in our graph and those points will be negative one comma one divided by a zero comma one and one comma A. Now, in our case, as I mentioned before, our A is equal to 15. So our points will be negative one comma one divided by 15 zero, comma one and one comma 15. And that will be it for my first recall point. My second recall point will deal with knowing if our function is increasing or decreasing. So if R A is greater than one F of X is increasing, and if zero is less than A is less than one, or basically, if A is between zero and one, then F of X is decreasing. And now for our case, we have a or 15 and is greater than one. Therefore, our F of X is increasing. And now finally, my third recall point will deal with a horizontal asom tilt. So the graph of A to the exponent X has and ace toads at Y equals zero or the X axis. So Y equals zero is the X axis. So we'll have the X axis here will function as a horizontal acid FT. So now that I have those three points, I know that I know three points that will be in my graph, I know that my graph is increasing and I know that I have an asym tilt at the X axis. So now I have a general idea of what my graph will look like and I can go ahead and graph it. So that's exactly what I'll do, I'll draw a Y axis and an X axis. And I'll have a point at zero comma one and then I'll have another point at one comma and finally another point at negative one comma one divided by 15. And I know that my function is increasing. So as I connect those dots from left to right, they should be increasing or going upwards. And then I know that to my left, I'll be approaching the X axis forever, but never touching it as it functions as an Asymptote. So once we connect all those three dots and we approach that x axis, we will have a general idea of what our graph should look like. So I hope that was helpful. And until next time.

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

Key Concepts

Exponential Functions

Graphing Techniques

Transformations of Functions

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