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:

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)

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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.

... distinguish between the two, using both a graph and a ... Find the inverse function: f(x) = 3 x^2 - 5. ... this is an example of a exponential function (the variable is ...

... 7. Solve the following logarithmic equation. ... 8. The function f(x)=4x/3x-5 is one to one. Find its inverse and check your answer. f-1(x)=_____. ...

... Also, graphically, log-log graphs can be easier ... Logarithms (which are the inverse functions to exponentials ... to determine when an exponential function will reach ...

... is a quadratic function and so its graph is a ... exchange y with x to write the inverse function as ... of a detailed explanation to answer exponential form, polynomial ...

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