3.1 Relations
3.2 Graphs
Objective: Find the Cartesian product of two sets.
Find the following Cartesian products.
A A X B, where A  {d , e}and B {1,2}
B C X C, where C  { p, q, r}
Objective: List ordered pairs from a Cartesian product that satisfy a
given relation.
Any set of ordered pairs selected from a Cartesian product is a relation.
Objective: List the domain and the range of a relation.
List the domain and the range of the relation
C {(a, 1), (b, 2), (c, 3), (e, 2)}.
D {(2, 2), (1, 1), (1,2), (1, 3)}.
Objective: Use set-builder notation to define a relation.
Objective: Use set-builder notation to define a relation.
E Use the set {1, 2, 3, . . . , 10}.Find {x|5 < x < 7}.
F Use the set Q X Q, where Q = {2, 3, 4, 5}.
Find {(x, y)|x > 2 and y > 3}.
Objective: Graph ordered pairs of a relation
Cartesian Coordinate System
Objective: Determine whether an ordered pair is a solution of an
equation.
Solution: An ordered pair such that when the
numbers are substituted for the variables,
a true equation is produced
Determine whether the given ordered pairs are
solutions to the equation y = 3x - 1:
G (7, 5)
H (7, 20)
I (0, 6)
Objective: Graph equations by plotting several solutions.
Graph the following relations
J y  2x  3
K y  x  3
2
HW #3.1-2
Pg 108-109 1-29 Odd, 30-34
Pg 114-115 29, 31, 37, 43-57
HW Quiz #3.1-2
Thursday, April 09, 2015
Pg 108-109
30b
Pg 108-109
30c
Pg 108-109
30d
Pg 114-115
37
Pg 108-109
30a
Pg 108-109
34
Pg 108-109
31c
Pg 114-115
37
Chapter 3
Relations, Functions, and Graphs
3.3 Functions
Objective: Recognize functions and their graphs.
A relation where each member of the domain is paired with exactly
one member of the range is a function.
Objective: Recognize functions and their graphs.
Which of the following relations are functions?
A
B
Objective: Recognize functions and their graphs.
Objective: Recognize functions and their graphs.
Function
Not a Function
Which of the following relations are functions?
C
D
Objective: Use function notation to find the value of functions.
FUNCTION MACHINE
f ( x)
Pronounced “f of x”
Objective: Use function notation to find the value of functions.
FUNCTION MACHINE
Objective: Use function notation to find the value of functions.
Objective: Use function notation to find the value of functions.
Objective: Use function notation to find the value of functions.
For the function h defined by h  x   3x  27, evaluate:
2
E h(5)
F h(2)
Consider g  {(0, 2),(2, 4),(1,0),(3, 4)} find:
G g (2)
H g (0)
Objective: Find the domain of a function, given a formula for the
function.
When the function in R X R is given by a formula, the domain is
understood to be all real numbers that are acceptable replacements.
Finding the domain of a function  2 rules
1. Cannot let 0 be in the denominator
2. Cannot take a square root of a negative number
Objective: Find the domain of a function, given a formula for the
function.
Find the domain of the following functions.
State the domain using set-builder notation
I f  x   2x  x
4
2
x2
J p  x 
( x  2)( x  4)
HW #3.3-4
Pg 120-121 1-27 odd, 30-36
Pg 125-126 3-9 Odd, 11, 17, 21,
25, 27, 36-42
HW Quiz #3.3-4
Thursday, April 09, 2015
Chapter 3
Relations, Functions, and Graphs
3.4 Graphs of Linear Functions
3.5 Slope
Objective: Find the slope of a line containing a given pair of points.
Slope is the measure of how steep a line is
Objective: Find the slope of a line containing a given pair of points.
Slope is the measure of how steep a line is
Objective: Find the slope of a line containing a given pair of points.
Objective: Find the slope of a line containing a given pair of points.
Objective: Find the slope of a line containing a given pair of points.
Objective: Find the slope of a line containing a given pair of points.
Objective: Use the point-slope equation to find an equation of a line. .
HW #3.4-5
Pg 125-126 3-9 Odd, 11, 17, 21,
25, 27, 36-42
Pg 131-132 3-39 Every Third
Problem, 45-55
Chapter 3
Relations, Functions, and Graphs
3.6 More Equations of Lines
Objective: Use the two point equation to find an equation of a line. .
Objective: Use the two point equation to find an equation of a line.
Objective: Use the two point equation to find an equation of a line.
Objective: Find the slope and y-intercept of a line, given the slopeintercept equation for the line.
Objective: Find the slope and y-intercept of a line, given the slopeintercept equation for the line.
Objective: Find the slope and y-intercept of a line, given the slopeintercept equation for the line.
Objective: Graph linear equations in slope-intercept form.
Objective: Graph linear equations in slope-intercept form.
Objective: Graph linear equations in slope-intercept form.
Chapter 3
Relations, Functions, and Graphs
3.7 Parallel and Perpendicular lines
Objective: Determine if two lines are parallel or perpendicular or
neither.
HW #3.6-7
Pg 136-137 3-45 Every Third
Problem, 48-59
Pg 141-142 1-29 odd, 30-32
HW Quiz #3.7
Thursday, April 09, 2015
Pg 142 23
Pg 142 25
Pg 142 30a
Pg 142 32
Pg 142 21
Pg 142 23
Pg 142 30b
Pg 142 32
Chapter 3
Relations, Functions, and Graphs
3.9 More Functions
First class postage for letters or packages is a
function of weight. For one ounce or less, the
postage is $0.41. For each additional ounce or
fraction of an ounce, $0.41 is due.
1. What is the postage for a 0.5 oz package?
2. What is the postage for a 0.7 oz package?
3. What is the postage for a 1 oz package?
4. What is the postage for a 1.5 oz package?
5. What is the postage for a 2 oz package?
6. What is the postage for a 2.5 oz package?
7. Sketch a graph of the weight of the package vs cost to ship
Objective: Graph special functions
A step function has a graph which resembles a set of stair steps.
Another example of a step function is the greatest
integer function f(x) = [x].
The greatest integer
function, f(x) = [x], is the
greatest integer that is less
than or equal to x.
Objective: Graph special functions
f ( x)  [ x]  1
f ( x)  [ x  1]
Objective: Graph special functions
Finding the absolute value of a number can also be thought of in
terms of a function, the absolute value function, f(x) = |x|.
Objective: Graph special functions
f ( x) | x | 1
f ( x) | x  1|
Sketch the graph of the following two functions
A f ( x)  [ x  1]
B f ( x) | x  1|
Objective: Find the composite of two functions
( f g )( x)  f ( g ( x))
For f ( x)  x  3and g ( x)  x  3find :
C f ( g (2))
D g ( f (4))
For p( x)  x 2 and q( x)  x  3find :
E p(q( x))
F q( p( x))
For f(x) = 3x + b and g(x) = 2x – 7 find f(g(x))
For f(x) = px + d find f(f(x))
For f(x) = 2x + 6 and g(x) = 3x + b find b such that f(g(x)) = g(f(x))
Graph | x |  | y | 1
HW #3.9
Pg 150-151 1-25 Odd, 26-51
HW Quiz #3.9
Thursday, April 09, 2015
Pg 150 26a
Pg 150 30
Pg 150 40
Pg 150 48
Pg 150 26b
Pg 150 32
Pg 150 42
Pg 150 48
Test Review
Objective: List the domain and the range of a relation.
Objective: Recognize functions and their graphs.
Objective: Use function notation to find the value of functions.
Objective: Find the domain of a function, given a formula for the
function.
Objective: Find the slope of a line containing a given pair of points.
Objective: Use the point-slope equation to find an equation of a line.
Objective: Graph linear equations in slope-intercept form.
Objective: Find the slope and y-intercept of a line, given the slopeintercept equation for the line.
Objective: Determine if two lines are parallel or perpendicular or neither.
Objective: Graph special functions
Objective: Find the composite of two functions
Objective: Find a linear function and use the equation to make
predictions
Part 1
For f(x) = 3x + b and g(x) = 2x – 7 find f(g(x))
For f(x) = px + d find f(f(x))
For f(x) = 2x + 6 and g(x) = 3x + b find b such that f(g(x)) = g(f(x))
Given that f is a linear function with f(4)=-5 and f(0) = 3,
write the equation that defines f.
Part 2
Show that the line containing the points (a, b) and (b, a) is
perpendicular to the line y = x. Also show that the midpoint of
(a, b) and (b, a) lies on the line y = x.
The equation 2x – y = C defines a family of lines, one line for
each value of C. On one set of coordinate axes, graph the
members of the family when C = -2, C= 0, and C= 4. Can you
draw any conclusion from the graph about each member of the
family? What about Cx +y = -4?
If two lines have the same slope but different x-intercepts, can
they have the same y-intercept?
If two lines have the same y-intercept, but different slopes, can
they have the same x-intercept?
The Greek method for finding the equation of a line tangent to a
circle used the fact that at any point on a circle the line containing
the center and the tangent line are perpendicular. Use this method
to find the equation of the line tangent to the circle x2 + y2 = 9 at
the point (1, 22).
Prove: If c  d and a and b are not both zero, then ax + by =c
and ax + by = d are parallel
HW #R-3
Pg 157 1-30 Study all challenge
problems
Find the area of an equilateral triangle