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!!!