For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
I am having trouble figuring out my points to plot on the graph.
e^x and e^2x
x = 0, e^0 = 1 e^2*0 = 1
x = 1, e^1 = 2.72, e^2 = 7.39
x = 2, e^2 = 2.72, e^4 = 54.6
x = 3, e^3 = 20.1, e^6 = 403
etc (diverge fast from each other)
ln x and ln 2x
do not try ln 0
x = 1 , ln 1 = 0, ln 2 = .693
x = 2 , ln 2 = .692 , ln 4 = 1.39
x = 3 , ln 3 = 1.1 , ln 6 = 1.79
(do not diverge from each other so fast)
.
.
.
x = 10 , ln 10 = 2.30 , ln 20 = 3.00
To graphically show the effect of doubling x for the exponential function ex and the logarithmic function log x, you can follow these steps:
1. Exponential Function (y = ex):
- Choose a few values of x and calculate the corresponding values of y using the exponential function y = ex. For example, take x = 1, 2, 3, and so on, and calculate y = e^x.
- Now, double each of the x-values you chose in the previous step to get new x-values. For example, if you chose x = 1, 2, 3, then the doubled values would be 2, 4, 6.
- Calculate the corresponding values of y for the doubled x-values using the exponential function y = e^x. For example, calculate y = e^2, e^4, and e^6.
- Plot the original points (x, y) and the new points (2x, y) on a graph.
- Connect the points with a smooth curve. You should notice that the doubled x-values result in rapidly increasing y-values.
2. Logarithmic Function (y = log x):
- Choose a few values of x and calculate the corresponding values of y using the logarithmic function y = log x. For example, take x = 1, 2, 3, and so on, and calculate y = log(x).
- Now, double each of the x-values you chose in the previous step to get new x-values. For example, if you chose x = 1, 2, 3, then the doubled values would be 2, 4, 6.
- Calculate the corresponding values of y for the doubled x-values using the logarithmic function y = log(x). For example, calculate y = log(2), log(4), and log(6).
- Plot the original points (x, y) and the new points (2x, y) on a graph.
- Connect the points with a smooth curve. You should notice that the doubled x-values result in slowly increasing y-values.
By following these steps and plotting the points, you should be able to visualize the effect of doubling x for the exponential function and the logarithmic function on the graph.