SOLUTION: I've been working on my homework and I have it all finished except for two graphing problems. I was wondering how to plot the graphs of the following functions: f(x)=(1/5)^x f(x

Algebra ->  Graphs -> SOLUTION: I've been working on my homework and I have it all finished except for two graphing problems. I was wondering how to plot the graphs of the following functions: f(x)=(1/5)^x f(x      Log On


   

Question 173237: I've been working on my homework and I have it all finished except for two graphing problems. I was wondering how to plot the graphs of the following functions:
f(x)=(1/5)^x
f(x)=4^x - 3
f(x)=7^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started.

# 1

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



-----------------------------------------------


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.






# 2

In order to graph f%28x%29=4%5E%28x-3%29, we need to plot some points:


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


Let's find the y value when x=0


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%5E%283%29 Flip the fraction to make the exponent positive


y=1%2F64 Cube 4 to get 64


y=0.015625 Divide.


So when x=0, then y=0.015625



-----------------------------------------------


Now 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%5E%282%29 Flip the fraction to make the exponent positive


y=1%2F16 Square 4 to get 16


y=0.0625 Divide.


So when x=1, then y=0.0625



-----------------------------------------------



Now 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%5E%281%29 Flip the fraction to make the exponent positive


y=1%2F4 Raise 4 to the first power to get 4


y=0.25 Divide.


So when x=2, then y=0.25



-----------------------------------------------



Now 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 Raise 4 to the zeroth power to get 1


So when x=3, then y=1



-----------------------------------------------


Now 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 Raise 4 to the first power to get 4


So when x=4, then y=4



-----------------------------------------------


Now let's find the y value when x=5


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


y=4%5E%285-3%29 Plug in x=5


y=4%5E%282%29 Subtract


y=16 Square 4 to get 16


So when x=5, then y=16



-----------------------------------------------


So we have the following values:


xy
00.015625
10.0625
20.25
31
44
516




Now let's plot these points





Now draw a curve through those points to graph f%28x%29=4%5E%28x-3%29




Note: once again, the graph does NOT cross or touch the x-axis. It just looks like that since the y values start off very small.