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a. Functions and their Graphs
b. Basic Business Mathematics
c. Logic
Liza L. MagalsoMathematics G11
General MathematicsCourse Outline
Real-Life FunctionsPiece-wise functions
Evaluation on functions
Liza L. MagalsoMathematics G11
June 16, 2016
General MathematicsFunctions
What we are about to learn…
identify functions from relations
evaluates a function
represents real-life situations using functions, including piece-wise functions
4
2. 5 + -8 =
7
Review: Operations on Functions
1. 3 + 4 =
3. -4 + -7 = -3-11
4. -2 + 8 = 6
5
2. 6 - 8 =3
Review: Operations on Functions
1. 5 - 2 =
3. -4 - 3 = -2-7
4. 7 - -5 = 12
6
2. (3) (-6) =20
Review: Operations on Functions
1. (5) (4) =
3. (-7) (4) = -18-28
4. (-5) (-3) =
15
7
2. 15 ÷ -3 =
5
Review: Operations on Functions
1. 20 ÷ 4 =
3. -8 ÷ -2 = -5 4
4. -30 ÷ 6 =
-5
Functions Functions relate an input to an output
Functions in real life: Output: Score in the test
Input: No. of hours studied
FunctionsFunctions in real life:
Give another real-life situations involving functions
Functions
Illustration of Functions:
b. mapping or arrow diagrama. set of ordered pair
c. graphing
Functions
a. set of ordered pair1. {(3,2), (4,0), (5,1), (2,3)} Function2. {(1,2), (0,3), (1,6), (5,4)}3. {(3,4), (3,0), (3,1), (3,3)}4. {(4,2), (3,2), (6,2), (5,2)}
Not Function
Not Function
Function
Functions
a. set of ordered pair ( x, y )x - First element Domain
y - Second Element RangeIndependent variable
Dependent variable
Functions
b. diagram345 Function
One-to-One Relation
abc
236
94
3
236
236
23
Function Not Function Not FunctionMany-to-One
RelationOne-to-Many
RelationNot all elements
are represented
Functions
c. graphing
Functionsc. graphing
16
FunctionsEvaluation on Functions
FunctionsEvaluation on Functions
h(-3) = (-3)2 -4(-3) + 9 = 9 + 12 + 9 = 30
Piece-wise Functions Functions in pieces
Piece-wise Functions
Piece-wise Functions
Piece-wise Functions
Functions
Answer Me:Is this relation a function?
1. {(1,3),(2,3),(3,3)}2. {(2,3),(2,3),(4,3)}3. {(-3,3),(-2,3),(-
5,3)}4. {(1,4),(2,4),(3,4)}
YesNoYesYes
Functions
Answer Me:Is this relation a function?
YesNo
Functions
Answer Me:Is this graph a function?
YesNo
Functions
Answer Me:Is this graph a function?
Functions
Answer Me:Find the value:
1. f(x) = 3x2 - 4x + 9
x = 0, x = -2
2. h(x) = 4x3 - 6x - 12
3. g(x) = 5x + 4
4. f(x) = x2 + 5x
f(0) = 9
f(-2) = 29
h(0) = -12
f(0) = 0
g(0) = 4
h(-2) = 32g(-2) = -
6f(-2) = -
6
Activity: Group Drill
• Function: (Oh Yes!) • Not Function: (Oh No!)
1. {(-2,3),(2,3),(-3,3)}
2. {(3,3),(2,2),(4,4)}
3. {(1,8),(1,5),(1,3)}
4. {(7,3),(8,3),(5,3)}
Oh Yes!
Oh Yes!
Oh No!
Oh Yes!
Activity: Group Drill• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!Oh Yes!
Oh No!
Activity: Group Drill• Function: (Oh Yes!) • Not Function: (Oh
No!)
Oh Yes! Oh No! Oh Yes!Oh No!
Activity: Group Drill• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!Oh Yes!
Oh No!
Functions
Find my value:
1. f(x) = 2x2 - 3x + 4 , f(0)?
2. h(x) = x3 - 3x - 3 , h(-2)
3. g(x) = 6x - 4 , g(3)
4. f(x) = 5x2 + 3x - 6, f(-3)
f(0) = 4
h(-2) = -5g(3) =
14f(-3) = 30
FunctionsAssessment:
A. Which of the following are functions
1. {(4,3),(-4,3),(3,3)}2. {(2,5),(4,4),(2,3)}
FunctionNot Function
Not Function Function
3. 4.
FunctionsAssessment:
B. Evaluate the following:
1. f(z) = z2 - 5z + 22. h(x) = 3x - 4
4
f(-2) = 16f(-2)
3. g(x) = 2x3 + 3x - 1
4. f(x) = x4 + 6x3 -3
f(0)
f(-3)
f(-1)
f(-0) = -1
f(-3) = -64
f(-1) = -8
Assignment:A. Find the following:
g(x) = x + 1 f(x) = x - 1
1. (g + f) (x)
5. (g f) (x)2. (g - f) (x)
4. (g ÷ f) (x)
3. (gf) (x)
Thank you!!!
