SOLUTION: Plot the graph of the following function f(x) = 4^x-3

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Question 150436: Plot the graph of the following function
f(x) = 4^x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Table of Contents:

Table
Graph

In order to graph y=4%5E%28x-3%29, we need to plot a few points.


Let's find the y value when x=0 note: you can start at any x value.


y=4%5E%28x-3%29 Start with the given equation.


y=4%5E%280-3%29 Plug in x=0.


y=4%5E%28-3%29 Subtract


y=1%2F4%5E3 Rewrite 4%5E%28-3%29 as 1%2F4%5E3


y=1%2F64 Evaluate 4%5E3 to get 64


y=0.016 Divide and simplify.


So when x=0, y=0.016. So we have the point (0,0.016).


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Let's find the y value when x=1


y=4%5E%28x-3%29 Start with the given equation.


y=4%5E%281-3%29 Plug in x=1.


y=4%5E%28-2%29 Subtract


y=1%2F4%5E2 Rewrite 4%5E%28-2%29 as 1%2F4%5E2


y=1%2F16 Evaluate 4%5E2 to get 16


y=0.063 Divide and simplify.


So when x=1, y=0.063. So we have the point (1,0.063).


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Let's find the y value when x=2


y=4%5E%28x-3%29 Start with the given equation.


y=4%5E%282-3%29 Plug in x=2.


y=4%5E%28-1%29 Subtract


y=1%2F4%5E1 Rewrite 4%5E%28-1%29 as 1%2F4%5E1


y=1%2F4 Evaluate 4%5E1 to get 4


y=0.25 Divide and simplify.


So when x=2, y=0.25. So we have the point (2,0.25).


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Let's find the y value when x=3


y=4%5E%28x-3%29 Start with the given equation.


y=4%5E%283-3%29 Plug in x=3.



y=4%5E%280%29 Subtract


y=1 Evaluate 4%5E0 to get 1


So when x=3, y=1. So we have the point (3,1).


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Let's find the y value when x=4


y=4%5E%28x-3%29 Start with the given equation.


y=4%5E%284-3%29 Plug in x=4.


y=4%5E%281%29 Subtract


y=4 Evaluate 4%5E1 to get 4


So when x=4, y=4. So we have the point (4,4).


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Now let's make a table of the values we just found.





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Table of Values:


TEST: 0



xy
00.016


10.063


20.25


31


44

Now let's plot these points:







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Graph:


Now draw a curve through all of the points to graph y=4%5E%28x-3%29:


Graph of y=4%5E%28x-3%29