Avon High School
Section: 1.1
ACE COLLEGE ALGEBRA II - NOTES
Graphs and Graphing Utilities
Mr. Record: Room ALC-129
Day 1 of 1
The 16th Century was a prolific time in the arenas or math and science.
A brand new branch of math tree was introduced, called analytic geometry,
when a Frenchman named René Descartes first used a rectangular coordinate
system.
This coordinate plane sometimes
called the Cartesian coordinate plane is
divided into four _____________
that are numbered as follows:
Rene Descartes
Graphs of Equations
.
Example 1
Graph y  4  x 2 on the coordinate plane provided by making a table of values and selecting
appropriate integer values for x.
y





x



















.
Example 2
Graph y  x on the coordinate plane provided by making a table of values and selecting
appropriate integer values for x.
y





x















Graphs of Equations Using a Graphing Utility
To the right is a screen shot (from the TI-Nspire CX calculator)
depicting the graph from Example 1.
At time it will be appropriate to state the viewing window of graphs
sketched on a calculator. This particular window is set at
[-6, 6, 1] by [-6, 6, 1]
What does each number mean?
. Example 3
Label the following coordinate system to reflect the viewing window
[-2, 3, 0.5] by [-10, 20, 5].
y-intercept: 4
x-intercept: -2
Note: When identifying a y-intercept, one can
simply state the value “4.” It is also acceptable
to state the location as the ordered pair (0,4).
The same idea holds for stating x-intercepts.
x-intercept: 2
Interpreting Information Given By Graphs
Example 4
Indicate which graph matches the given statement.
a. A bicycle valve’s distance from the ground as a boy rides at a constant speed.
A)
B)
C)
D)
b. A child swings on a swing, as a parent watches from the front of the swing.
A)
.
B)
C)
D)
Perform the given operation for each expression.
a.
x  3 x2  x  6

x2  4 x2  6 x  9
b.
x2  2x  1 x2  x  2

x2  x
3x 2  3
Adding and Subtracting Rational Expressions
For this lesson, I will illustrate the worst case scenario – no common denominator.
Finding the Least Common Denominator
Follow these steps when you are faced with adding or subtracting rational expressions.
1. Factor each denominator completely.
2. List all factors of the first denominator.
3. Add to the list in Step 2 any factors of the subsequent denominators that are different.
4. The product of the result from Step 3 will be your common denominator.
. Example 4
a.
Perform the given operation for each expression.
x3 x 2

x 5 x 5
b.
x
x4

x  10 x  25 2 x  10
2
Complex Rational Expressions
Complex rational expressions, often called _________________________ have numerators and/or
denominators containing one or more rational expressions.
Example 5
a.
1 3

x 2
1 3

x 4
Simplify.
b.
1
1

x7 x
7