Download Alg 2, 2-1

Chapter 2
Section 1
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
1996
20.5
20.8
1997
1998
20.6
20.9
1999
2000
20.5
20.5
2001
20.4
Year
Fuel Efficiency
(mi/gal)
1995
1996
20.5
20.8
1997
1998
20.6
20.9
1999
2000
20.5
20.5
2001
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
2
12.5
16
4
22
6
9
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
–4
0
–1
1
2
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
(2, 5)
(1, 2)
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.
Answer:
(0, –1)
(–1, –4)
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.
Answer:
(2, 5)
(1, 2)
Yes, the equation
represents
a function.
(0, –1)
(–1, –4)
Answer:
a.
Graph
b.
Find the domain and range.
Answer:
c.
The domain and range
are both all real numbers.
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
Then sketch the
the corresponding values for x.
graph, connecting the points with a smooth curve.
x
y
5
–2
2
–1
1
0
2
1
5
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
(5, 2)
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.
(2, 1)
(1, 0)
(2, –1)
Answer: The domain is
The range is all
real numbers.
.
(5, –2)
Determine whether the relation is a function.
x
y
5
–2
2
–1
1
0
2
1
5
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
Answer:
a.
Graph
b.
Find the domain and range.
Answer:
The domain is
{x| x  –3}. The range
c.
is all
real numbers.
Determine
whether
the
relation is a function.
Answer:
No, the equation
represent a function.
does not
Given
, find
Original function
Substitute.
Simplify.
Answer:
Given
find
Original function
Substitute.
Multiply.
Simplify.
Answer:
Given
, find
Original function
Substitute.
Answer:
Given
find each value.
and
a.
Answer:
6
Answer:
0.625
b.
c.
Answer: