Question 580442
To graph on this given interval, we simply plug in values of x that are between -3 and 3 to get corresponding values of y. 



These x and y values will pair up to make a series of points that will be plotted on a coordinate system.


From there, you just draw a curve through all the points (the best you can) to graph y = 3^x



So when x = -3, then...


y = 3^x


y = 3^(-3)


y = 1/(3^3)


y = 1/27


y = 0.037037


So we have one point (-3, 0.037037)

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and when x = -2, then...


y = 3^x


y = 3^(-2)


y = 1/(3^2)


y = 1/9


y = 0.1111


So we have another point (-2, 0.1111)

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and when x = -1, then...


y = 3^x


y = 3^(-1)


y = 1/(3^1)


y = 1/3


y = 0.3333


So we have another point (-1, 0.3333)

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and when x = 0, then...


y = 3^x


y = 3^(0)


y = 1 ... Note: any number (except 0) to the zeroth power is 1.



So we have another point (0, 1)

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and when x = 1, then...


y = 3^x


y = 3^(1)


y = 3 ... Note: any number to the first power is that same number



So we have another point (1, 3)

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and when x = 2, then...


y = 3^x


y = 3^(2)


y = 9



So we have another point (2, 9)

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and finally, when x = 3, then...


y = 3^x


y = 3^(3)


y = 27



So we have another point (3, 27)

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Now we have the following points 


(-3, 0.037037), (-2, 0.1111), (-1, 0.3333), (0, 1), (1, 3), (2, 9), (3, 27)



Now plot them on a coordinate grid:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/graph1-2.png">


Now draw a curve (as best you can) through all of the points to graph y = 3^x on the interval [-3, 3]



Note: take notice as the red graph of y = 3^x stops at (3,27) because it's at the end of the interval (the same applies to the other end of the graph).



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/graph2-2.png">