Algebra II A – Guided Notes
2-1 Guided Notes
Relations and Functions
Name ________________________________
Period ______________
Learning Matrix Goal #1: I can identify x & y intercepts in a graph or a set of ordered pairs.
Learning Matrix Goal #2: I can use the definition of function to explain why there can be only one yintercept.
Learning Matrix Goal #3: I can identify increasing and decreasing intervals of a table or graph.
Learning Matrix Goal #4: I can identify the domain and range of a relation.
Learning Matrix Goal #5: I can explain how the domain and range of a function are represented in its
graph.
Learning Matrix Goal #6: I can evalute a function at a given value.
Learning Matrix Goal #7: I can identify and explain the dependent and indepent variables.
Learning Matrix Goal #8: I can describe and identify both functions and one-to-one functions.
How do relations and functions apply to biology? Look at the table on p. 56 of your textbook. Now
ask yourself this: What is the difference between average lifetime and maximum lifetime?
Why can you be sure that the second number in the ordered pairs for this data is always greater
than or equal to the first?
Copy Coordinate Plane from page 56 (bottom right)
Define vocabulary in your own words:
Ordered pairs-
Cartesian coordinate plane-
Quadrants-
Relation-
Domain-
Function-
Mapping-
One-to-one function
Complete the box p. 57
Concept Summary
Functions
Example 1 Domain and Range
State the domain and range of the relation shown in the graph. Is the relation a function?
You can use the _______________________________ to determine whether a relation is a function
Your Turn
Graph the following relation. State the domain and range. Is the relation a function?
{(-4,0), (-3,1), (0,-2), (1,2), (3,3)}
Your Turn
Explain why the set of order pairs {(9,3), (9,-3), (4,2), (3,-2)} is not a function
Key Concept
Vertical Line Test
Words:
Models:
When two points on the graph of a relation are intersected by a vertical line, this means those two
points have the same ____ value but different ____ values.
Study Tip
Vertical Line Test
You can use a pencil to represent a vertical line. Slowly move the pencil to the right
across the graph to see if it intersects the graph at more than one point.
Example 2 Vertical Line Test
Geography
The table shows the population of the state of Indiana over the last several decades. Graph this
information and determine whether it represents a function. (Create a small coordinate plane from graph
paper and attach it here).
Year
1950
1960
1970
1980
1990
2000
Population (millions)
3.9
4.7
5.2
5.5
5.5
6.1
Notice also that each year is paired with only one population value. (So every ____ value only has one
____ value)
Your Turn
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. (Create a small coordinate plane from
graph paper and attach it here).
Year
1995
1996
1997
1998
1999
2000
2001
Fuel efficiency (mi/gal)
20.5
20.8
20.6
20.9
20.5
20.5
20.4
Example 3 Graph is a Line. (Paraphrase the following statements).
a. Graph the relation represented by y = 2x + 1 Draw the table and the graph.
b. Find the domain and range.
x can be ____________________, so there is an ____________________ of ________________.
Every ___________________ is the x-coordinate of some point on the line.
Also every, ________________________ is the y-coordinate of some point on the line.
So the domain and range are both ____________________________.
Symbolized in set notation by:
Symbolized in interval notation by:
c. Determine whether the relation is a function
The graph passes the _______________________________.
Also, for each ______ value, there is exactly one _______ value, so the equation represents a
_________________.
Your Turn
a. Graph the relation represented by y = 3x -1.
b. Find the domain and range. Show in both set and interval notation.
c. Determine whether the relation is a function.
Example 4 Graph is a Curve
a. Graph the relation represented by x =
- 2. Draw the tables and graph.
In this case, it is easier to choose _____ values and then find the corresponding ______ values.
Now sketch the graph by _______________________________________________________.
b. Find the domain and range.
Every __________________ is the _____ coordinate of some point on the graph. So the range is
___________________.
Symbolized in set notation by _________________
Symbolized in interval notation by _____________________
Only real numbers greater than or equal to ____ are ____ coordinate points on the graph. So the
domain is ___________________ (symbolized in set notation) and
___________________ (symbolized in interval notation)
c. Determine whether the relation is a function.
Your Turn
a. Graph the relation represented by x =
+ 1.
b. Find the domain and range. Show in both set and interval notation.
c. Determine whether the relation is a function.
Study Tip
Reading Math
Suppose you have a job
that pays by the hour.
Since you pay depends
on the number of hours
you work, you might
say that your pay is a
function of the number
of hours you work.
Your pay is the
dependent variable, and
the number of hours
you work is the
independent variable.
(because how much
you earn depends on
how long you work)
Define the following vocabulary:
Independent variable-
Dependent variable-
Functional notation-
Example 5 Evaluate a Function
Given f (x) =
and g (x) = 0.5
a.
f (-3)
, find each value.
b. g (2.8)
c. f (3z)
Your Turn
Given f (x) =
and h (x) = 0.3
, find each value.
a. f (-2)
b. h(1.6)
c. f(2t)
Now you need to complete page 60 # 1-3, 17-22, 23-31 odd, 42-53.
When assignment is complete, you should check your solutions (get them from the
solutions folder). Mark correct problems with a star. Mark incorrect problems with
an X and them make corrections on the problems that you had incorrect.