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

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) (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 , we need to plot some points:

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

Let's find the y value when

Start with the given equation

Plug in

Flip the fraction to make the exponent positive.

Reduce

Raise to the first power to get 5

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Raise to the zeroth power to get 1

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Raise to the first power to get

Divide

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Square to get

Divide

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Cube to get

Divide

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Raise to the fourth power to get

Divide

So when , then

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

So we have the following values:

x	y
-1	5
0	1
1	0.2
2	0.04
3	0.08
4	0.0016

Now let's plot these points

Now draw a curve through those points to graph

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 , we need to plot some points:

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

Let's find the y value when

Start with the given equation

Plug in

Subtract

Flip the fraction to make the exponent positive

Cube 4 to get 64

Divide.

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Subtract

Flip the fraction to make the exponent positive

Square 4 to get 16

Divide.

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Subtract

Flip the fraction to make the exponent positive

Raise 4 to the first power to get 4

Divide.

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Subtract

Raise 4 to the zeroth power to get 1

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Subtract

Raise 4 to the first power to get 4

So when , then

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

Now let's find the y value when

Start with the given equation

Plug in

Subtract

Square 4 to get 16

So when , then

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

So we have the following values:

x	y
0	0.015625
1	0.0625
2	0.25
3	1
4	4
5	16

Now let's plot these points

Now draw a curve through those points to graph

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.
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