5.2 relations & functions. 5.2 – relations & functions evaluating functions remember, the...
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5.2
Relations & Functions
5.2 – Relations & Functions
Evaluating functions Remember, the DOMAIN is the set of
INPUT values and the RANGE is the set of OUTPUT values.
y = 3x + 4
inputoutput
Another way to remember them is…The domain is the
set of 1st coordinates of the ordered pairs.
The range is the
set of 2nd coordinates of the ordered pairs.
A relation is a
set of ordered pairs.
Given the relation {(3,2), (1,6), (-2,0)},
find the domain and range.
Domain = {3, 1, -2}
Range = {2, 6, 0}
The relation {(2,1), (-1,3), (0,4)} can be shown by either……
1) a table.
2) a mapping.
3) a graph.
x y
2-10
134
2-10
134
Given the following table, show the relation, domain, range, and mapping.
x -1 0 4 7y 3 6 -1 3
Relation = {(-1,3), (0,6), (4,-1), (7,3)}Domain = {-1, 0, 4, 7}Range = {3, 6, -1, 3}
Mappingx -1 0 4 7y 3 6 -1 3
You do not need to write 3 twice in the range!
-1047
36-1
What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)}
1. {2, 3, 4, 4}
2. {1, 2, 3, 1}
3. {2, 3, 4}
4. {1, 2, 3}
5. {1, 2, 3, 4}
Answer Now
What is the range of the relation{(2,1), (4,2), (3,3), (4,1)}
1. {2, 3, 4, 4}
2. {1, 2, 3, 1}
3. {2, 3, 4}
4. {1, 2, 3}
5. {1, 2, 3, 4}
Answer Now
Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x).
Write the relation and the inverse.
Relation = {(-1,-6), (3,-4), (3,2), (4,2)}
Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}
-134
-6-42
Write the inverse of the mapping.
-3
43-12
1. {(4,-3),(2,-3),(3,-3),(-1,-3)}
2. {(-3,4),(-3,3),(-3,-1),(-3,2)}
3. {-3}
4. {-1, 2, 3, 4} Answer Now
Functions
A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).
f(x)x y
Function Notation
Output
InputName of Function
y f x
Determine whether each relation is a function.1. {(2, 3), (3, 0), (5, 2), (4, 3)}
YES, every domain is different!
f(x)2 3
f(x)3 0
f(x)5 2
f(x)4 3
Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
f(x)4 1
f(x)5 2
f(x)5 3
f(x)6 6
f(x)1 9
NO, 5 is paired with 2 numbers!
Is this relation a function?{(1,3), (2,3), (3,3)}
1. Yes
2. No
Answer Now
Vertical Line Test (pencil test)
If any vertical line passes through more than one point of the graph, then that relation is not a function.
Are these functions?
FUNCTION! FUNCTION! NOPE!
Vertical Line Test
NO WAY!FUNCTION!
FUNCTION!
NO!
Is this a graph of a function?
1. Yes
2. No
Answer Now
Given f(x) = 3x - 2, find:1) f(3)
2) f(-2)
3(3)-23 7
3(-2)-2-2 -8
= 7
= -8
Given h(z) = z2 - 4z + 9, find h(-3)
(-3)2-4(-3)+9-3 30
9 + 12 + 9
h(-3) = 30
Given g(x) = x2 – 2, find g(4)
Answer Now
1. 2
2. 6
3. 14
4. 18
Given f(x) = 2x + 1, find-4[f(3) – f(1)]
Answer Now
1. -40
2. -16
3. -8
4. 4
5.2 – Relations & Functions
Example: Evaluate the function rule f(a) = -3a + 5 to
find the range of the function for the domain {-3, 1, 4}.
5.2 – Relations & Functions
To solve this, all you have to do is plug ALL of the numbers in for a and solve.
f(a) = -3a + 5
f(-3) = -3(-3) + 5
f(-3) = 9 + 5
f(-3) = 14
5.2 – Relations & Functions
Once you have done this for ALL of the numbers, you would write your answer from smallest to largest like the following: {-7, 2, 14}
5.2 – Relations & Functions
Make a table for f(n) = -2n + 7. Use 1, 2, 3, and 4 as domain values.
2
n f(n)
1
2
3
4