5'2 Relations and Functions

1
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
  x-coordinates.
• The range of a relation is the set of second
  coordinates the y-coordinates.

2
Finding Domain and Range

• Find the domain and range of the ordered pairs
  listed for the giraffe data.
• (18 , 4.25) (20 , 4.40)
• (21 , 5.25)
• (14 , 5.00)
• (18 , 4.85)
• Domain 14, 18, 20, 21
• Range 4.25, 4.40, 4.85, 5.00, 5.25

Giraffes
Age
Height
3
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.

4
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.

5
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.

6
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.

7
Using a Mapping Diagram

• Determine whether each relation is a function.
• b. (-2 , -1) , (-1 , 0) , (6 , 3) , (-2 , 1)
• Domain Range
• -2 -1
• -1 0
• 6 1
• 3
• The domain value corresponds to two range values
  -1 and 1.
• The relation is not a function.

8
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.

9
Evaluating a Function Rule

• Evaluate f(n) -3n 10 for n 6.
• f (n) -3n 10
• f (6) -3(6) 10
• f (6) -18 10
• f (6) -28
• Evaluate y -2x2 7 for x -4
• y -2(-4)2 7
• y -2(16) 7
• y -32 7
• y -25

10
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

11
More Practice!!!

• Textbook p. 244 2 26 even.