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

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Accepted Answer

Hello everybody. I hope you're doing. All right. Today, today we're going to be looking at this math question that states plot the given function on the rectangular cord in its system where our function is FX is equal to seven, the fraction seven divided by eight and that fraction to the exponent X. Now we looking at a question like this. The first thing I want to ask myself is what is the parent function here? So in our case, our parent function will be F of X is equal to A to the exponent X where A is equal to seven divided by A. So A this is a general formula for our function A could be any, any constant, any number. In our case, it's seven divided by eight. So now that I know my parent function A to the X one X I can ask myself what are different rules and different things we know about this graph. So I'm going to recall that. So first, I'll have rule number one or recall number one where when we have the function A to the exponent X I know the graph will have points at negative one comma one divided by a, a point at zero, comma one and a point at one comma eight. And like I mentioned R A is equal to seven divided by eight. So our points will be at negative one comma eight over seven. Since we had one divided by A and our A is a fraction, we just do the reciprocal of that fraction, then we'll continue to have a point at zero comma one. And finally, we have a point at one comma seven divided by eight. And that'll be our first point here. Our first recall point. My second recall point is that if A is greater than one F of X is increasing, and we also know that if zero is less than A is less than one, which just means if A is between zero and one F of X is decreasing. In our case, we have that zero is less than seven divided by eight is less than one, which means we have a function that is decreasing and that'll be our second point. So now our second recall point, so now we have three points that we can know for our graph and we know that our function is a decreasing function. Now, my third recall point here is that for A, to the exponent X graph, the X axis is an A tote. So now that we've made these three recall points, we have a general idea of what our graph should look like and we can go ahead and draw this graph. So we draw a Y axis and an X axis and we'll have points at zero comma one, we have a point at one Karma seven divided by eight. So that will be a very small Y that will be one comma seven divided by eight. And then we also had a point at negative one come up eight divided by seven, which is a little above one. So it should be above our zero comma Y point, not a lot but ever so slightly. And we'll label that as negative one comma eight divided by seven. And we recall that this is a decreasing function. So when we connect the dots or the points here, we should be decreasing. And remember that we will approach the X axis forever but never touch it because it isn't as tote. And that should be a general idea of what a graph should look like. So I hope that was helpful. And until next time.

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

Key Concepts

Exponential Functions

Plotting Points for Graphing

Asymptotes and End Behavior

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

Key Concepts

Exponential Functions

Plotting Points for Graphing

Asymptotes and End Behavior

Watch next

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