We're asked to graph the function
f of x is equal to 5x minus 4.
And we'll do it by really just sampling some points
from the domain and seeing what value our function takes.
And then we'll just graph those points.
And then we'll connect the dots and see what forms.
And there's other ways to do this,
but this is the most simple or the most basic way.
So if you look at this function right over here,
it's actually defined for any real number
that you stick there for x.
So when we talk about sampling the domain,
we can actually pick any real number for x.
I'm actually going to pick real numbers that
are fairly small in magnitude so that they're easy to graph.
So I don't have to plot 8 billion on a number line
over here.
So let's draw ourselves some simple graph paper.
Let's call that the x-axis.
Let's call that the y-axis, or, actually, I
should call it the y is equal to f of x.
Whatever my x is, I input it into this function definition.
It'll tell me what the function value is.
It'll tell me f of x.
And we're going to say y is equal to that.
Now let's draw a little table here to try out some values.
So let's say that this is x values and then this is f of x.
And I can even say this is my y values, which
are going to be equal to f of x.
So let's start with-- I'm going to try negative 2,
negative 1, 0, 1, and 2.
So let's try negative 2 first.
if x is equal to negative 2, what is f of x?
Well, f of x is going to be 5 times negative 2 minus 4.
So it's 5 times negative 2 minus 4,
which is equal to negative 10 minus 4, which is negative 14.
So let me plot that over here.
And let me-- actually, maybe I'm going
to have a slightly more scrunched up scale
on the y-axis.
And, actually, let me give myself some space
so that I can go further down.
Let me clear this.
Give myself a little bit of space.
So I have a feeling that I'll be using a lot of negative values
since I just got all the way down to negative 14.
So let me go further down here.
And then let me mark off some increments over here.
So let's say that this is negative 5.
This is negative 10.
And this is negative 15.
And then this would be positive 5.
And then this would be positive 10.
So we have when x is negative 2, f of x is equal to negative 14,
which is right about there.
So that is negative 14.
So that right over there is the point negative 2,
negative 14, which we got right from that.
Now, let's try another point.
Let's try negative 1.
When x is negative 1, f of x is 5 times negative 1 minus 4.
5 times negative 1 is negative 5, minus 4 is negative 9.
So when x is negative1, f of x is negative 9.
So negative 9 is right about here.
So this is negative 9.
So this is the point negative 1 negative 9
that is on the graph of f of x.
And now let's try 0.
When x is 0, f of x is going to be 5 times 0 minus 4.
Well, that's just 0 minus 4, which is equal to negative 4.
So when x is 0, f of x is equal to negative 4.
So that's negative 4 right over there.
And actually, our point is going to be sitting right over there.
That is 0, negative 4.
I wrote it to the left of the point.
Let's keep going.
Let's what happens when x is equal to 1.
When x is equal to 1, f of x is equal to 5 times 1 minus 4.
5 times 1 is 5 , minus 4 is equal to 1.
So we get to the point 1,1.
So 1 and then 1 is right about there.
So this is the point 1,1.
And then let's just try one more.
Let's see what happens when x is equal to 2.
Then, f of x is 5 times 2 minus 4, which is 10 minus 4,
which is equal to 6.
So we have when x is equal to 2, f of x is equal to 6.
So it's right about there.
That's 6 right there.
So this is the point 2, 6.
So once again, these are just sample points from the domain.
This isn't the entire domain.
But it gives us enough points to kind of see
the general structure of the graph.
If we connect the dots, we see a line forming.
So If we connect the dots-- let me draw.
So if we connect the dots, it looks something like this.
And my shaky hand makes it look a little bit curvy,
but it should be an absolute straight line.
If I had this on really good graph paper
and I have had a ruler, you will see
that this is a straight line.
And it would keep going on and on and on.
And I want to make it clear that we just
sampled points from the domain.
But we could take any point in the domain, which we already
said is all real numbers.
So if we took right over here.
If we said 1.5 you could see.
And if you graph 1.5, f of 1.5 it
should sit on that line right over there.
If you graphed f of negative 0.5-- so this is negative 0.5.
If you graphed f of negative 0.5,
it should sit on the line right over there.
But we're done.
We have graphed the function f of x is equal to 5x minus 4.