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Exponential Functions and their Inverse and Graphs

Please provide graphs.

1. One example of an exponential function is f(x) = 4x. Its inverse can be found this way:
y = 4x
x = 4y
x = log4y
y = log4x
An example of points to plot to create the graphs are given:

F(x) F1(x)
(1, 4) (4, 1)
(0, 1) (1, 0)
(2, 16) (16, 2)
(-1, .25) (.25, -1)

3. For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
include the reasons for graphically representing the effect in a particular way. scan the graph you've plotted and post it along with your response.

X Ex E2x
0 1 1
1 2.72 7.39
2 7.39 54.6
3 20.09 303.43
4 54.6 2980.96

X Log(x) Log(2x)
0 Undefined Undefined
1 0 .3
2 .3 .6
10 1 1.3
20 1.3 1.6
With the first set, the graph rises twice as fast when doubled, making it much steeper. However, with the second set, when x is doubled it only raises the graph by .3. This is because log (a*b) = log (a) + log(b). Since log(2)=.3 (or 100.3 = 2), the graph is raised by this constant regardless of the value of x)

Solution Preview

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1. One example of an exponential function is f(x) = 4^x. Its ...

Solution Summary

This solution deals with exponential functions. I have shown what happens to the graph of some exponential functions when the argument of the function is doubled. Solution also includes three graphs.

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