SOLUTION: Hello Jim, f(x)= (1/5)^x help please I have to graph this???

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Question 173133: Hello Jim,
f(x)= (1/5)^x help please I have to graph this???
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph f%28x%29=%281%2F5%29%5Ex, we need to plot some points:


Note: I'll use "y" in place of f(x)



Let's find the y value when x=-1


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E%28-1%29 Plug in x=-1


y=%285%2F1%29%5E1 Flip the fraction to make the exponent positive.


y=%285%29%5E1 Reduce


y=5 Raise 5 to the first power to get 5


So when x=-1, then y=5



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Now let's find the y value when x=0


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E0 Plug in x=0


y=1 Raise 1%2F5 to the zeroth power to get 1


So when x=0, then y=1



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Now let's find the y value when x=1


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E1 Plug in x=1


y=1%2F5 Raise 1%2F5 to the first power to get 1%2F5


y=0.2 Divide


So when x=1, then y=0.2



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Now let's find the y value when x=2


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E2 Plug in x=2


y=1%2F25 Square 1%2F5 to get %281%2F5%29%5E2=%281%2F5%29%281%2F5%29=1%2F25


y=0.04 Divide


So when x=2, then y=0.04



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Now let's find the y value when x=3


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E3 Plug in x=3


y=1%2F125 Cube 1%2F5 to get %281%2F5%29%5E3=%281%2F5%29%281%2F5%29%281%2F5%29=1%2F125


y=0.008 Divide


So when x=3, then y=0.008



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Now let's find the y value when x=4


y=%281%2F5%29%5Ex Start with the given equation


y=%281%2F5%29%5E4 Plug in x=4


y=1%2F625 Raise 1%2F5 to the fourth power to get %281%2F5%29%5E4=%281%2F5%29%281%2F5%29%281%2F5%29%281%2F5%29=1%2F625


y=0.0016 Divide


So when x=4, then y=0.0016



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So we have the following values:


xy
-15
01
10.2
20.04
30.08
40.0016




Now let's plot these points





Now draw a curve through those points to graph f%28x%29=%281%2F5%29%5Ex





Note: the graph does NOT cross or touch the x-axis. It just looks like that since the y values become very small.