Schema Activator (FORM A,C)
1. List the 4 ways to represent
relations.
2. Explain how do you determine if a
given relation is a function or not.
3. Give an example of a relation that is
NOT a function; represent it in 4
different ways.
Interval Notation
Write using interval notation
Domain and Range
• Algebra in Motion
What is the domain of this function?
What is the range of this function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5
The graph shows the path of a golf ball
What is the range
of this function?
F 0 < y < 100
G 0 ≤ y ≤ 100
H 0≤ x≤5
J 0≤ x≤5
What is the domain?
A -2 < y ≤ 2
B -4 ≤ x ≤ 6
C -4 < y ≤ 2
D -2 < x ≤ 6
What is the domain of this function?
A -1 ≤ x ≤ 5
B -1 ≤ x ≤ 9
C 2≤x≤5
D 0≤ y≤ 9
Domain?
Range?
Domain?
Range?
Sometimes you will be asked to
determine a REASONABLE domain or
range
The average daily high temperature for the
month of May is represented by the function
t = 0.2n + 80
Where n is the date of the month. May has 31
days. What is a reasonable estimate of the
domain?
Answer: 1 ≤ n ≤ 31
What is a reasonable estimate of the range
Answer: See next slide
Our function rule is:
t = 0.2n + 80
Our domain is 1 ≤ n ≤ 31
Our smallest possible n is 1
Our largest possible n is 31
To find the range, substitute 1 into the equation
and solve. Then substitute 31 into the
equation and solve.
Our function rule is:
t = 0.2n + 80
Substitute a 1
t = 0.2n + 80
t = 0.2(1) + 80
t = 0.2 + 80
t = 80.2
Substitute a 31
t = 0.2n + 80
t = 0.2(31) + 80
t = 6.2 + 80
t = 86.2
Reasonable range is 80.2 ≤ t ≤ 86.2
Linear Equations from Graphs and
Function Notation
What do you remember?
• Slope Intercept Form
• Point Slope Form
• Standard Form
Equations from Graphs and
Function Notation
Equations from Graphs and
Function Notation
Find the equation of the line that goes
through the given points.
1) Write the equation of the line that
goes through the given points:
2) Write the standard form of the
equation of the line described:
Functions in Real World
Sketch a reasonable graph for each situation:
1) You take a roast beef from the refrigerator and
put it into a hot oven.
2) The temperature of your cup of coffee is related
to how long it has been cooling.
3) You climb on the top of the school and drop
your Algebra book off. The distance the book is
above the ground depends on the number of
seconds that have passed since you dropped it.
Graphs of equations with 2 variables
2 x  3 y  15
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Find a solution of the equation
How many solutions does this equation have?
“Smart choices”
Table of values
Dependent variable
Independent variable
Non Linear Graphs
y  0.2 x
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2
Table of values
Graphing calculator
Setting the window
Table set
Domain
Range