SOLUTION: Oh dear God please help me!!! We are studying Graphs of Exponential and Logarithmic Functions and I am so lost I'm about to send out the hound dogs, but seriously if someone could

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Question 150386: Oh dear God please help me!!! We are studying Graphs of Exponential and Logarithmic Functions and I am so lost I'm about to send out the hound dogs, but seriously if someone could please help just get me started I would greatly appreciate it.
I am supposed to Plot the graphs of the following functions:I don't understand how
1. f(x) = 7x this x variable is actually an exponent so it is 7 to the x power
2. f(x) = 4x - 3 the x-3 here is also an exponent so it reads 4 to the x-3 power
3. f(x) = (1/5)x this is actually 1/5 to the x power again the x is an exponent
4. f(x) = log3x
Thank you guys for always helping me out. I can't wait till I get this degree so I can help yall out with some $$$.
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started.

# 1

Table of Contents:

Table
Graph

In order to graph , we need to plot a few points.


Let's find the y value when note: you can start at any x value.


Start with the given equation.


Plug in .



Rewrite as


Evaluate to get 49


Divide and simplify.


So when , . So we have the point (-2,0.02).


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


Let's find the y value when


Start with the given equation.


Plug in .


Rewrite as


Evaluate to get 7


Divide and simplify.


So when , . So we have the point (-1,0.143).


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


Let's find the y value when


Start with the given equation.


Plug in .


Evaluate to get 1


So when , . So we have the point (0,1).


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


Let's find the y value when


Start with the given equation.


Plug in .


Evaluate to get 7


So when , . So we have the point (1,7).


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


Now let's make a table of the values we just found.





Jump to Table of Contents

Table of Values:


TEST: -2



xy
-20.02


-10.143


01


17

Now let's plot these points:







Jump to Table of Contents

Graph:


Now draw a curve through all of the points to graph :


Graph of




# 2

Table of Contents:

Table
Graph

In order to graph , we need to plot a few points.


Let's find the y value when note: you can start at any x value.


Start with the given equation.


Plug in .


Subtract


Rewrite as


Evaluate to get


Divide and simplify.


So when , . So we have the point (0,0.016).


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


Let's find the y value when


Start with the given equation.


Plug in .


Subtract


Rewrite as


Evaluate to get


Divide and simplify.


So when , . So we have the point (1,0.063).


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


Let's find the y value when


Start with the given equation.


Plug in .


Subtract


Rewrite as


Evaluate to get


Divide and simplify.


So when , . So we have the point (2,0.25).


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


Let's find the y value when


Start with the given equation.


Plug in .



Subtract


Evaluate to get


So when , . So we have the point (3,1).


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


Let's find the y value when


Start with the given equation.


Plug in .


Subtract


Evaluate to get


So when , . So we have the point (4,4).


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


Now let's make a table of the values we just found.





Jump to Table of Contents

Table of Values:


TEST: 0



xy
00.016


10.063


20.25


31


44

Now let's plot these points:







Jump to Table of Contents

Graph:


Now draw a curve through all of the points to graph :


Graph of
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
$$$, huh...WOW!!

plotting the graphs is straight forward (a graphing calculator would be a big help)
__ the f(x) values are on the vertical (y) axis and the x values are on the horizontal axis
__ find the f(x) values by "plugging in" values for x

1. f(x)=7^x __ when x=0, f(x)=1 (this is the y-intercept) __ when x is 1, f(x)=7
__ as x becomes a large NEGATIVE value, f(x) approaches zero (horizontal asymptote)

2. f(x)=4^(x-3) __ when x=3, the exponent is 0 so f(x)=1 __ when x=0, f(x)=4^(-3) or 1/64
__ same general shape as #1 with different y-intercept

3. f(x)=(1/5)^x __ when x=0, f(x)=1
__ as x becomes a large POSITIVE value, f(x) approaches zero (horizontal asymptote)
__ this graph is sort of a "mirror image" of #'s 1 and 2

4. logarithms are NOT defined for negative quantities, so this graph is only on the right-hand side of the vertical axis
__ as x approaches zero (very small fractions), f(x) approaches negative infinity (vertical asymptote)
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