Transcript 5.2 Relations and Functions • A relation is a set of ordered pairs. • The domain of a relation is the set.

5.2 Relations and Functions
• A relation is a set of ordered pairs.
• The domain of a relation is the set of first
coordinates of the ordered pairs – the xcoordinates.
• The range of a relation is the set of second
coordinates – the y-coordinates.
Finding Domain and Range
• Find the domain and range of the ordered pairs listed
for the giraffe data.
Giraffes
Age
(years)
18
Height
(meters)
4.25
20
4.40
21
5.25
14
5.00
Age
Height
(18 , 4.25)
(20 , 4.40)
(21 , 5.25)
(14 , 5.00)
(18 , 4.85)
18
4.85
Domain: {14, 18, 20, 21}
Range: {4.25, 4.40, 4.85, 5.00, 5.25}
Function
• A function is a relation that assigns
exactly one value in the range to each
value in the domain.
– You can tell if a relation is a function by
analyzing the graph of a relation using the
vertical-line test.
• If any vertical line passes through more than one
point of the graph, the relation is not a function.
Using the Vertical-Line Test
• Determine whether the relation {(3 , 0), (-2 , 1),
(0 , -1), (-3 , 2), (3 , 2)} is a function.
• Step 1 – graph the ordered pairs on a
coordinate plane.
Vertical-Line Test
• Step 2 – use the Vertical – Line test.
• A vertical line passes through both (3 , 0) and (3
, 2), so the relation is not a function.
Using a Mapping Diagram
• Determine whether each relation is a function.
a. {(11 , -2) , (12 , -1) , (13 , -2) , (20 , 7)}
Domain
Range
11
-2
12
-1
13
7
20
There is no value in the domain that corresponds
to more than one value of the range.
The relation is a function.
Using a Mapping Diagram
• Determine whether each relation is a function.
b. {(-2 , -1) , (-1 , 0) , (6 , 3) , (-2 , 1)}
Domain
-2
-1
6
Range
-1
0
1
3
The domain value corresponds to two range
values -1 and 1.
The relation is not a function.
Evaluating Functions
• A function rule is an equation that describes a
function.
– The domain is the set of input values.
– The range is the set of output values.
• A function is in function notation when you
use f(x) to indicate the outputs.
– You read f(x) as “f of x” or “f is a function of x”.
– The notations g(x) and h(x) also indicate functions
of x.
Evaluating a Function Rule
a. Evaluate f(n) = -3n – 10 for n = 6.
f (n) = -3n – 10
f (6) = -3(6) – 10
f (6) = -18 – 10
f (6) = -28
b. Evaluate y = -2x2 + 7 for x = -4
y = -2(-4)2 + 7
y = -2(16) + 7
y = -32 + 7
y = -25
Finding the Range
• Evaluate the function rule f(a) = -3a + 5 to find
the range of the function for the domain
{-3 , 1 , 4}.
a. f(a) = -3a + 5
f(-3) = -3(-3) + 5
f(-3) = 14
b. f(a) = -3a + 5
f(1) = -3(1) + 5
f(1) = 2
c. f(a) = -3a + 5
f(4) = -3(4) + 5
f(4) = -7
More Practice!!!
• Textbook – p. 244 #2 – 26 even.
• Homework – Workbook p. 325