Download HA2 Relations and Functions

September 14,2010
Objectives
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Students will be able to:
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Analyze and graph relations,
Find functional values.
Terminology
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Relation:
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Domain:
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Is the set of all x-coordinates of a relation.
Range:
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Set of ordered pairs.
Is the set of all y-coordinates of a relation.
Function:
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Is a special type of relation in which each element
of the domain is not repeated with an element of
the range.
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One-to-One Function:
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Vertical Line Test:
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A function where each element of the range is
paired with exactly one element of the domain.
Is used to determined a function by drawing a
vertical line any where on the relation (graph) and
checking for two repeated domain (x) values.
Independent Variable:
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The domain values.
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Dependent Variable:
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The range value.
Functional Notation:
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F(x), this is used in place of y= when talking or
working with functions.
State the domain and range
of the relation shown in the
graph. Is the relation a
function?
The relation is {(1, 2), (3, 3),
(0, –2), (–4, 0), (–3, 1)}.
Answer: The domain is
{–4, –3, 0, 1, 3}. The range
is {–2, 0, 1, 2, 3}. Each member
of the domain is paired with exactly one member of the
range, so this relation is a function.
State the domain and range
of the relation shown in the
graph. Is the relation a
function?
Answer: The domain is
{–3, 0, 2, 3}. The range
is {–2, –1, 0, 1}. Yes, the
relation is a function.
Transportation The table
shows the average fuel
efficiency in miles per
gallon for light trucks for
several years. Graph this
information and
determine whether it
represents a function.
Year
Fuel Efficiency
(mi/gal)
1995
20.5
1996
1997
1998
1999
20.8
20.6
20.9
20.5
2000
2001
20.5
20.4
Year
Fuel Efficiency
(mi/gal)
1995
20.5
1996
1997
1998
1999
20.8
20.6
20.9
20.5
2000
2001
20.5
20.4
Use the vertical line test. Notice that no vertical
line can be drawn that contains more than one
of the data points.
Answer: Yes, this relation is a function.
Health The table shows
the average weight of a
baby for several months
during the first year.
Graph this information
and determine whether it
represents a function.
Age
(months)
Weight
(pounds)
1
12.5
2
4
6
9
16
22
24
25
12
26
Answer:
Yes, this relation is a function.
Graph the relation represented by
Make a table of values to find ordered pairs that satisfy the
equation. Choose values for x and find the corresponding
values for y. Then graph the ordered pairs.
x
y
–1
0
1
2
–4
–1
2
5
(2, 5)
(1, 2)
(0, –1)
(–1, –4)
Find the domain and range.
Since x can be any real number,
there is an infinite number of
ordered pairs that can be
graphed. All of them lie on the
line shown. Notice that every
real number is the x-coordinate
of some point on the line. Also,
every real number is the
y-coordinate of some point
on the line.
(2, 5)
(1, 2)
(0, –1)
(–1, –4)
Answer: The domain and range are both all
real numbers.
Determine whether the relation is a function.
This graph passes the vertical
line test. For each x value, there
is exactly one y value.
(2, 5)
(1, 2)
Answer: Yes, the equation
represents
a function.
(0, –1)
(–1, –4)
a. Graph
Answer:
b. Find the domain and range.
Answer: The domain and range
are both all real numbers.
c. Determine whether the
relation is a function.
Answer: Yes, the equation
is a function.
Graph the relation represented by
Make a table. In this case, it is easier to choose y values
and then find the corresponding values for x. Then sketch
the graph, connecting the points with a smooth curve.
x
y
5
2
1
2
5
–2
–1
0
1
2
(5, 2)
(2, 1)
(1, 0)
(2, –1)
(5, –2)
Find the domain and range.
Every real number is the
y-coordinate of some point on
the graph, so the range is all real
numbers. But, only real numbers
that are greater than or equal to
1 are x-coordinates of points on
the graph.
Answer: The domain is
The range is all
real numbers.
(5, 2)
(2, 1)
(1, 0)
(2, –1)
(5, –2)
.
Determine whether the relation is a function.
x
y
5
2
1
2
5
–2
–1
0
1
2
(5, 2)
(2, 1)
(1, 0)
(2, –1)
(5, –2)
You can see from the table and the vertical line test that
there are two y values for each x value except x = 1.
Answer: The equation
a function.
does not represent
a. Graph
Answer:
b. Find the domain and range.
Answer: The domain is
{x|x  –3}. The range
is all real numbers.
c. Determine whether the
relation is a function.
Answer: No, the equation
represent a function.
does not
Class Work
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Guided Practice
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Page 47 (1-8)
Exit Question
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1) Write an example of a one-to-one
function.
2) Write a relation and then state the domain
and range of the relation.
3) Graph a relation and show that it is NOT a
function.
Homework
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Pages 48
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(22-30,42,44-46) DUE 9/16