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Welcome to our class.
Hello. I am your math professor,
Barbara Rademacher.
Let's review Algebra 1 and 2.
Let's review graphing.
We are going to graph the line
x - 4y = 8 by plotting the
x- and y- intercepts.
Recall that the x-intercept is where the line
crosses the x-axis,
and the y-intercept is where the line crosses the y-axis.
The easiest way to find the intercepts of a
line is to make a table like this.
If x = 0, we find the y-intercept.
Substitute zero for x in the original equation
and solve for y.
If x=0, then
y = -2.
So the y-intercept is the point
(0, -2). YOU MUST WRITE POINTS WITH
PARENTHESES.
If y=0, then the point we find will be
the x-intercept.
Substitute zero for y in
the original equation.
Then, solve for x.
If y = 0, then x = 8.
The x-intercept is the point (8,0).
Let's graph the line.
Enlarge the graph by clicking on the magnifying glass icon.
Click on the line tool.
Put your cursor on one of the two points you calculated, and click.
Then, find the second point you calculated, and click.
Click on Save and then on Check Answer.
We got it right! Fantastic!
Now, in homework problem #2,
Let's graph with the graphing calculator.
We are told what values to use
and what equation to graph.
Go to TBLSTART by clicking on the 2nd button and then on the WINDOW button.
Reset TblStart to -3.
TBL is already set to 1. That is the difference
between each succeeding value of x.
Now, click on the Y= button.
Type the required equation into Y1.
Click on the GRAPH button.
We have a cupped-down parabola.
Click on the 2nd button and then on the GRAPH button.
Find the y-coordinates that accompany the x- coordinates in the question.
If x is -3, then
y is -7.
If x is -2,
then y is -2.
If x is -1,
then y is 1.
Now, find the correct graph on the right.
It is D.
In homework problem #3, we review the
fundamental definitions of domain and range.
The domain consists of the set
of all the x-coordinates without repetition.
Use a comma between
each x-coordinate.
No need to list the second occurrence of 9.
The range is the set of all the y-coordinates
without repetition.
Separate each number with a comma.
The relation is not a function.
Whenever x-coordinates are repeated like 9
was repeated, the relation is NOT
a function.
In homework problem #4, we are going to
evaluate functions.
For g(6), we will substitute 6 for every x.
In b)
we will substitute 1 for every x.
g(1) = 0.
In c), we will substitute -3 for every x.
Oh, no! Zero in the denominator is
undefined.
In d), we will substitute
-18.75
for every x.
Time for a calculator!
Let's divide the numerator
by the denominator.
Click on the MATH button
Then click on the ENTER key twice.
There is the answer for d).
Part e) is a little different.
We will be evaluating with variables.
We will substitute (x+h)
for every x.
That's the answer.
That's as far as we can go.
Lets enter the answers in the answer boxes.
Undefined also means
does not exist.
Homework problem #5 is extremely
eye-opening.
What is the Y-COORDINATE on the graph
where X = -4?
Find out with me.
-6.
This is one of the things functions are really saying.
Go to the graph. If x = -3, what is the y- coordinate?
Let's make the graph easier to see.
What is the y-coordinate of the point on the
graph where x = -2?
Fantastic!
Is this the graph of a function.
The answer is yes if no two points occur
one directly above the other.
Let's enlarge.
One point looks like it is directly above the
other.
The graph is not the graph of a function.
To find the domain of a rational (fraction)
function, we must find the values of x
that will cause the denominator to equal
zero, and take those values OUT of the domain.
Set the denominator equal to zero and
solve the resulting equation.
I factored, but you can also use the
quadratic formula.
-9 and -3 MUST be removed from the domain.
Well done!