Exponential Functions - Problem 3

We are graphing exponential functions today and here is an example; graph y equals the cube root of 2 to the x. Now, I don’t like the look of root cube root of 2, I want to make this look easier. So I’m going to use the properties of exponents to write this in a different way.

The cube root of 2 is the same as 2 to the 1/3 power. So I have 2 to the 1/3 to the x. I use the parallel power property of exponents, and I get 2 to the x over 3, much easier to graph. So I’m going to graph y equals 2 to the x over 3. Let me make a quick table.

Now here, when I choose values of x to plug in, I’m going to chose multiples of 3. The arithmetic is going to be the easiest so I’m going to chose numbers like -3, 0, 3, 6. When I plug in -3 I get 2 to the -3 over 3, 2 to the -1, which is 1/2. When I plug in 0, I get 2 to the 0 over 3, 2 to the 0 which is 1. When I plug in 3, I get 2 to the 3 over 3 to the 1 which is 2. And plugging in 6, I get 2 to the 6 over 3, 2²,4. So I got four points I’m going to plot these and draw my curve.

(-3,1/2) right here (0,1), (3,2), (6,4) and now I connect these with a nice smooth curve. And there we have it; y equals cube root of 2 to the x power.