Hey, guys.
Welcome to Algebra 1.
Today's lesson is going
to focus on finding values
for elements in a domain
of linear functions.
Your knowledge of how
to evaluate expressions
will come in handy
during this lesson.
Ready to get started?
Let's go.

(Describer) She uses a stylus on a screen.

So to warm up to exactly
what we'll be doing here,
I want to throw back
to finding the Y-intercept
of liner functions.
So, given this function,
F of X equals 5X minus 10,
if I were being asked
to find the Y-intercept--
so I have in mind
"Y-intercept."
That means that--
write myself a note here...
that X is definitely 0
and Y has some numerical value.
So knowing what we do about
slope intercept form,
we kind of already know
that the Y-intercept's
going to be negative 10,
but I want to show you
what I mean about warming up
for what we're doing.
So if I actually
went through this problem
and replaced my X with 0,
I would have F of 0
equals 5 times 0
minus 10, right?
Because I'm substituting 0
for the value X.
So 5 times 0 is 0,
minus 10.
And 0 minus 10
is just negative 10.
So I know this function
has a Y-intercept
of negative 10, right?
Because we substituted
that value 0 for X.
Now, you're able to substitute
any value in the domain
of a function for X
in order to determine
what the output value is
that corresponds
to that value.
Let me show you want I mean.
Look at this example.
We still have our function
F of X equals 5X minus 10,
but now we need to find F of 3;
that's how we read that--
that's what that
interprets to mean.
You see how the 3
took the place of the X,
and we're just looking at that
F of X part of our function?
That indicates that you need
to replace X with 3
in your function,
and see what you get
when you work the problem out.
This is what I mean.
My function is F of X
equals 5X minus 10.
So I'm going to find F of 3.
I'm going to substitute 3
every time I see X.
So I am going to have
5 times 3 minus 10.
5 times 3,
that's 15, minus 10.
15 minus 10, that's 5.
So that means
I can say, okay,
this function evaluated at 3,
or F of 3, equals 5.
And you're all done.
You just evaluated
this function at 3
in order to determine what its
output value is, okay?
So let's try another one.
We'll stick with function
F of X equals 5X minus 10,
but this time we're going
to find F of negative 2.
So each time we see an X
in our function,
we're going to substitute
negative 2.
So F of negative 2
equals 5
times negative 2 minus 10.
So 5 times negative 2,
that's negative 10.
And then minus 10.
Negative 10 minus 10...
is negative 20.
So this function,
evaluated at 2--
I'm sorry,
evaluated at negative 2--
is negative 20.
So F of negative 2
is negative 20.
And you're all done.
You see, it's just a matter
of substituting
whatever you're given
for the value of X
into your function,
working everything out,
and then just seeing
what you get at the end, okay?
It is time for you
to try a couple.
You have the function
F of X equals 6X minus 4,
and you need to find F of 1
and find F of negative 2.
Press pause,
take a few minutes,
work through these problems,
and when you're ready
to compare your answers
with me, press play.

(Describer) Titles: Given: F of x equals 6x minus 4.
Letter a: Find f of 1
Letter b: Find f of negative 2.

(female narrator)
Given: F of X equals
6X minus 4.
Letter A: Find F of 1.
Letter B:
Find F of negative 2.
All right?
Let's see what you got.
Let's move these little...
hiders away here.
Okay, so F of 1--
let's delete that.
F of 1 equals 2.
And F of negative 2--
let's delete that--
is negative 16.
If you want to see
how I got this,
I'll show you my work.
Okay, so to find F of 1--
scroll down a little bit--
I just replaced X
with 1 in my function.
So I have--
oops, get the pen...
So I have F of 1
equals 6 times 1
minus 4.
So 6 times 1 is 6 minus 4,
and then 6 minus 4 is 2.
So that's how I got
the F of 1 equals 2, okay?
It's a matter of what math users
like to call "plug and chug."
Just substitute that value
for 1 in there for X
and see what you get
for your answer.
Now, in B, what I did
is I followed
that same process.
I substituted X
with a negative 2.
So F of negative 2
equals 6 times
negative 2 minus 4.
6 times negative 2
is negative 12 minus 4.
And negative 12 minus 4
is negative 16.
So that's how I found
that F of negative 2
equals negative 16.
Just follow
that same process.
Substitute negative 2
in there for X,
and then see what you get
at the end, okay?
Okay, let's look at some graphs
of some linear functions,
and I'll show you how
to figure out the same thing,
how you can be given
a value for X
and figure out
what your output value is.
So here you need
to find F of 4.
When you see something
like that,
they're asking you
to figure out,
when X is 4, what is Y?
That's how you interpret
that "find F of 4."
We'll go to 4 on our X-axis.
I'll just scroll a bit.
So I'm going to go to 4,
so one, two, three, four.
Then look for your function.
I see here's my line.
In order to hit my line
I have to drop down...
So here X is 4
and my line's underneath me,
so I'll drop down.
And I need to find
that Y value,
right there, whenever X is 4.
Basically I want to know
what's this point, right here?

(Describer) ...where the lines cross.

Okay.
And if I trace this
to the Y-axis,
then I'll know the Y value.

(Describer) She draws across.

It's negative 1.
And that makes sense

because this is the point
(4, negative 1).
So when my input value is 4,
my output value
is negative 1, okay?
I've evaluated
this function at 4
and been able to tell what
my output value is there, okay?
So then I could come back to my
problem and say, F of 4...
is negative 1.
Because when X is 4,
Y is negative 1, okay?
Let's try another one,
make sure you got
the hang of that.
Okay, now you're being asked
to find F of negative 1.
I'll scroll down a bit.
Okay.
Let me get
my highlighter out.
So when X is negative 1--
that's my point here--
I see that my line,
again, it's underneath me.
So I'm going to drop down.

(Describer) She draws down to the line.

And I see that I hit that line,
right there.
I'm going to darken
that point, okay?
So when X is negative 1,
I need to find
this Y value here.
I'm going to trace this over
to the Y-axis
and see where I'm at.
And it looks like I'm at
negative 3.
I can say, all right,

well, this is the point,
(negative 1, negative 3).
So when X is negative 1,
Y is negative 3.
Then I could come back
to my problem and say, okay,
then F of negative 1
is negative 3.
When negative 1's my input,
negative 3
is my output, okay?
And you were able
to tell that
from looking at the graph
of that function.
All right? Good job.
Now you try one,
see how you do.
You're being asked to find
F of negative 3.
Press pause,
take a few minutes,
and analyze this graph.
When you're ready to compare
your answer against mine,
press play.

(Describer) Title: find f of negative 3.
The line on the graph crosses the x-axis at 4 and a half, and crosses the y-axis at 3.

(female narrator)
Find F of negative 3.
The line in the graph crosses
the X-axis at 4-1/2,
and crosses the Y-axis at 3.
All right,
let's see how you did.
Let me switch
to my highlighter.
I'm being asked
to find F of negative 3.
I'll go to negative 3
on my X-axis--
negative 1,
negative 2, negative 3--
this time my line
is above me,
so I'm going to go up
and I end up right there.

(Describer) She draws up to the line.

I'm going to darken
that point.
And then I'll trace over
to the Y-axis
so I can see exactly
what's going on there.

(Describer) She draws over.

I see when
I'm at negative 3 for X,
I'm at one, two,
three, four, five for Y.

This is the point
(negative 3, 5).
So I can say, all right,
then F of negative 3...
is 5.
Because when X
is negative 3,
Y has a value of 5,
all right?
Good job on that!
Okay, guys, you've reached
the end of our lesson
on finding values for elements
in the domain
of our linear functions.
I hope you saw how
your knowledge
of the coordinate plane,
and of function notation,
and how to evaluate expressions
came in handy for you.
See you back here soon
for more Algebra 1. Bye!

(Describer) Accessibility provided by the US Department of Education.