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ENGINEERING MATHEMATICS-II

DIPLOMA IN ELECTRICAL ENGINEERING

2nd SEMESTER

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SATYA PRAGYAN SWAIN

ASST. PROFESSOR

GANDHI INSTITUTE FOR EDUCATION AND TECHNOLOGY, BANIATANGI, BHUBANESWAR

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Warm Up

  1. Evaluate f(x)= 5x-3 for x=4

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  • Graph the following point on a graph. *Label Each*

(1, 3), (-1, 0), (1/2, -4), (0, 4)

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  1. Solve for y: f(x)= 5x-3 for x=4

f(4)= 5(4)-3

f(4)=20-3

f(4)=17

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b) Graph the following point on a graph. *Label Each*

(1, 3), (-1, 0), (1/2, -4), (0, 4)

(1, 3)

(-1, 0)

(0, 4)

(1/2, -4)

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Relations

  • What is a relationship?

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  • In math a relation is a connection between a set of inputs and a set of outputs

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Review on Relations and Functions

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Representations� (other than equations)

  1. Ordered pairs:

(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)

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2) Table:

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x

-3

-1

0

2

4

5

y

-2

4

1

-5

5

0

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3) Graph

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(-3, -2)

(5, 0)

(0, 1)

(-1, 4)

(4, 5)

(2, -5)

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4) Mapping

(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)

-3

-1

5

2

4

0

-5

-2

0

1

4

5

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4) Mapping (another way)

(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)

-3

-1

0

2

4

5

-5

-2

0

1

4

5

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Domain and Range

  • Domain- All inputs
  • Range- All outputs

(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)

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Domain: -3, 5, 0, -1, 4, -5

Range: -5, -2, 0, 1, 4, 5

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Function

  • A function is a special kind of relation where every input goes to exactly one output
    • It’s PREDICTABLE!

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*Can be written using Function Notation:

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One-to-one

  • Every input has a unique output

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Onto

  • Every output has an input

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Discrete vs. Continuous

  • Discrete relation: A relation where the domain is a set of individual points
  • Continuous relation: A relation that can be graphed with a line or smooth curve

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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{(2,3), (3,4), (5,1), (6,2), (2,4)}

Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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{(2,3), (3,4), (5,1), (6,2), (3,3)}

Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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The number of employees a company had in each year from 2004 to 2009 were 25, 28, 34, 31, 27, and 29.

Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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Domain?

Range?

Function?

One to one?

Onto?

Discrete or Continuous?

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