SOLUTION: I need help with this: graph the following functions separately: f(x)=5^x f(x)=-2+e^x

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Question 87833: I need help with this: graph the following functions separately:
f(x)=5^x
f(x)=-2+e^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
f%28x%29=5%5Ex Start with the given expression
In order to plot an exponential function, we need to plot some points
We can start at any x value, so lets start at x=-5

f%28-5%29=5%5E-5 Plug in x=-5

f%28-5%29=0.00032 Raise 5 to the negative fifth power to get 0.00032

So when x=-5, y=0.00032. So our first point is (-5,0.00032)


----Now lets find another point----
f%28-4%29=5%5E-4 Plug in x=-4

f%28-4%29=0.0016 Raise 5 to the negative fourth power to get 0.0016

So when x=-4, y=0.0016. So our second point is (-4,0.0016)


----Now lets find another point----
f%28-3%29=5%5E-3 Plug in x=-3

f%28-3%29=0.008 Raise 5 to the negative third power to get 0.008

So when x=-3, y=0.008. So our third point is (-3,0.008)


----Now lets find another point----
f%28-2%29=5%5E-2 Plug in x=-2

f%28-2%29=0.04 Raise 5 to the negative second power to get 0.04

So when x=-2, y=0.04. So our fourth point is (-2,0.04)


----Now lets find another point----
f%28-1%29=5%5E-1 Plug in x=-1

f%28-1%29=0.2 Raise 5 to the negative first power to get 0.2

So when x=-1, y=0.2. So our fifth point is (-1,0.2)


----Now lets find another point----
f%280%29=5%5E0 Plug in x=0

f%280%29=1 Raise 5 to the zeroth power to get 1

So when x=0, y=1. So our sixth point is (0,1)


----Now lets find another point----
f%281%29=5%5E1 Plug in x=1

f%281%29=5 Raise 5 to the first power to get 5

So when x=1, y=5. So our seventh point is (1,5)


----Now lets find another point----
f%282%29=5%5E2 Plug in x=2

f%282%29=25 Raise 5 to the second power to get 25

So when x=2, y=25. So our eighth point is (2,25)


----Now lets find another point----
f%283%29=5%5E3 Plug in x=3

f%283%29=125 Raise 5 to the third power to get 125

So when x=3, y=125. So our ninth point is (3,125)


----Now lets find another point----
f%284%29=5%5E4 Plug in x=4

f%284%29=625 Raise 5 to the fourth power to get 625

So when x=4, y=625. So our tenth point is (4,625)


----Now lets find another point----
f%285%29=5%5E5 Plug in x=5

f%285%29=3125 Raise 5 to the fifth power to get 3125

So when x=5, y=3125. So our eleventh point is (5,3125)



===============================================================================

Now lets make a table of the values we have calculated 



 xy



 -50.00032
 

 -40.0016
 

 -30.008
 

 -20.04
 

 -10.2
 

 01
 

 15
 

 225
 

 3125
 

 4625
 

 53125
Now plot the points



Connect the points to form the graph y=5%5Ex
Graph of y=5%5Ex through the points solved for earlier

-----------------------------------------------------------------------------
#2
f%28x%29=-2%2Be%5Ex

f%28x%29=e%5Ex-2 Rearrange


In order to plot an exponential function, we need to plot some points
We can start at any x value, so lets start at x=-5

f%28-5%29=e%5E-5-2 Plug in x=-5

f%28-5%29=0.007-2 Raise e (note: e=2.71828182846) to the negative fifth power to get 0.007

f%28-5%29=-1.993 Combine like terms 0.007 and -2 to get -1.993

So when x=-5, y=-1.993. So our first point is (-5,-1.993)


----Now lets find another point----
f%28-4%29=e%5E-4-2 Plug in x=-4

f%28-4%29=0.018-2 Raise e to the negative fourth power to get 0.018

f%28-4%29=-1.982 Combine like terms 0.018 and -2 to get -1.982

So when x=-4, y=-1.982. So our second point is (-4,-1.982)


----Now lets find another point----
f%28-3%29=e%5E-3-2 Plug in x=-3

f%28-3%29=0.05-2 Raise e to the negative third power to get 0.05

f%28-3%29=-1.95 Combine like terms 0.05 and -2 to get -1.95

So when x=-3, y=-1.95. So our third point is (-3,-1.95)


----Now lets find another point----
f%28-2%29=e%5E-2-2 Plug in x=-2

f%28-2%29=0.135-2 Raise e to the negative second power to get 0.135

f%28-2%29=-1.865 Combine like terms 0.135 and -2 to get -1.865

So when x=-2, y=-1.865. So our fourth point is (-2,-1.865)


----Now lets find another point----
f%28-1%29=e%5E-1-2 Plug in x=-1

f%28-1%29=0.368-2 Raise e to the negative first power to get 0.368

f%28-1%29=-1.632 Combine like terms 0.368 and -2 to get -1.632

So when x=-1, y=-1.632. So our fifth point is (-1,-1.632)


----Now lets find another point----
f%280%29=e%5E0-2 Plug in x=0

f%280%29=1-2 Raise e to the zeroth power to get 1

f%280%29=-1 Combine like terms 1 and -2 to get -1

So when x=0, y=-1. So our sixth point is (0,-1)


----Now lets find another point----
f%281%29=e%5E1-2 Plug in x=1

f%281%29=2.718-2 Raise e to the first power to get 2.718

f%281%29=0.718 Combine like terms 2.718 and -2 to get 0.718

So when x=1, y=0.718. So our seventh point is (1,0.718)


----Now lets find another point----
f%282%29=e%5E2-2 Plug in x=2

f%282%29=7.389-2 Raise e to the second power to get 7.389

f%282%29=5.389 Combine like terms 7.389 and -2 to get 5.389

So when x=2, y=5.389. So our eighth point is (2,5.389)


----Now lets find another point----
f%283%29=e%5E3-2 Plug in x=3

f%283%29=20.086-2 Raise e to the third power to get 20.086

f%283%29=18.086 Combine like terms 20.086 and -2 to get 18.086

So when x=3, y=18.086. So our ninth point is (3,18.086)


----Now lets find another point----
f%284%29=e%5E4-2 Plug in x=4

f%284%29=54.598-2 Raise e to the fourth power to get 54.598

f%284%29=52.598 Combine like terms 54.598 and -2 to get 52.598

So when x=4, y=52.598. So our tenth point is (4,52.598)


----Now lets find another point----
f%285%29=e%5E5-2 Plug in x=5

f%285%29=148.413-2 Raise e to the fifth power to get 148.413

f%285%29=146.413 Combine like terms 148.413 and -2 to get 146.413

So when x=5, y=146.413. So our eleventh point is (5,146.413)



===============================================================================

Now lets make a table of the values we have calculated 



 xy



 -5-1.993
 

 -4-1.982
 

 -3-1.95
 

 -2-1.865
 

 -1-1.632
 

 0-1
 

 10.718
 

 25.389
 

 318.086
 

 452.598
 

 5146.413
Now plot the points



Connect the points to form the graph y=e%5Ex-2
Graph of y=e%5Ex-2 through the points solved for earlier

If this seems like a lot of work, you can reduce the number of points to work with