Exponential and Logarithmic Functions
PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
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.