Question 580442: Hey I'm just so lost, my older sister tried helping me but she can't remember what to do. I would greatly appreciate your help! (I also greatly NEED it) hahaa By the way I'm not sure if I picked the right topic...but I tried. anyways it's bookwork it says:
Sketch each graph using as values of x the integers in the given interval.
y=3^x,[-3,3]
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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:
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).
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