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

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) (Show Source): You can put this solution on YOUR website!
#1
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

Plug in

Raise 5 to the negative fifth power to get 0.00032

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

----Now lets find another point----
Plug in

Raise 5 to the negative fourth power to get 0.0016

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

----Now lets find another point----
Plug in

Raise 5 to the negative third power to get 0.008

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

----Now lets find another point----
Plug in

Raise 5 to the negative second power to get 0.04

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

----Now lets find another point----
Plug in

Raise 5 to the negative first power to get 0.2

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

----Now lets find another point----
Plug in

Raise 5 to the zeroth power to get 1

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

----Now lets find another point----
Plug in

Raise 5 to the first power to get 5

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

----Now lets find another point----
Plug in

Raise 5 to the second power to get 25

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

----Now lets find another point----
Plug in

Raise 5 to the third power to get 125

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

----Now lets find another point----
Plug in

Raise 5 to the fourth power to get 625

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

----Now lets find another point----
Plug in

Raise 5 to the fifth power to get 3125

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

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

Now lets make a table of the values we have calculated

Now plot the points

Connect the points to form the graph
Graph of through the points solved for earlier

-----------------------------------------------------------------------------
#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

Plug in

Raise e (note: e=2.71828182846) to the negative fifth power to get 0.007

Combine like terms 0.007 and -2 to get -1.993

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

----Now lets find another point----
Plug in

Raise e to the negative fourth power to get 0.018

Combine like terms 0.018 and -2 to get -1.982

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

----Now lets find another point----
Plug in

Raise e to the negative third power to get 0.05

Combine like terms 0.05 and -2 to get -1.95

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

----Now lets find another point----
Plug in

Raise e to the negative second power to get 0.135

Combine like terms 0.135 and -2 to get -1.865

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

----Now lets find another point----
Plug in

Raise e to the negative first power to get 0.368

Combine like terms 0.368 and -2 to get -1.632

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

----Now lets find another point----
Plug in

Raise e to the zeroth power to get 1

Combine like terms 1 and -2 to get -1

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

----Now lets find another point----
Plug in

Raise e to the first power to get 2.718

Combine like terms 2.718 and -2 to get 0.718

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

----Now lets find another point----
Plug in

Raise e to the second power to get 7.389

Combine like terms 7.389 and -2 to get 5.389

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

----Now lets find another point----
Plug in

Raise e to the third power to get 20.086

Combine like terms 20.086 and -2 to get 18.086

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

----Now lets find another point----
Plug in

Raise e to the fourth power to get 54.598

Combine like terms 54.598 and -2 to get 52.598

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

----Now lets find another point----
Plug in

Raise e to the fifth power to get 148.413

Combine like terms 148.413 and -2 to get 146.413

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

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

Now lets make a table of the values we have calculated

Now plot the points

Connect the points to form the graph
Graph of through the points solved for earlier

If this seems like a lot of work, you can reduce the number of points to work with
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x	y
-5	-1.993
-4	-1.982
-3	-1.95
-2	-1.865
-1	-1.632
0	-1
1	0.718
2	5.389
3	18.086
4	52.598
5	146.413