a. Functions and their Graphs b. Basic Business Mathematics c. Logic Liza L. Magalso Mathematics G11 General Mathematics Course Outline
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!!!