Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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Transcript of Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

Page 1: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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Page 2: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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2 Dimensional graphs

3 Dimensional graphs

Functions and graphs

Graphing functions

Page 3: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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-5 -4 -3 -2 -1 1 2 3 4 5 x

-5

-4

-3

-2

-1

1

2

3

4

5 y

y = x

y = x2

y = x3

y = x4

Page 4: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

x2 + y2 = 9

Circle Ellipse

x2 + = 19__y

2

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Three dimensionsThree dimensions

+ + = 14__y

2

4__x

2

4__z

2

Sphere

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Three dimensionsThree dimensions

x2 + + z2 = 19__y

2

Cigar shape

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Three dimensionsThree dimensions

Flying saucer + y2 + = 1 9__z

2

9__x

2

Page 8: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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-5 -4 -3 -2 -1 1 2 3 4 5 x

-5

-4

-3

-2

-1

1

2

3

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5 y

y = x + 1

By observation a lot can be deduced about a graph, if both powers of x and y

are one, it is always a straight line

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-5 -4 -3 -2 -1 1 2 3 4 5 x

-5

-4

-3

-2

-1

1

2

3

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5 y

y + 1 = x2

If one power of x or y is one and the other is two it’s a curve with

one bend

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-5 -4 -3 -2 -1 1 2 3 4 5 x

-5

-4

-3

-2

-1

1

2

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5 y

y = x3 – 3x2 – x + 3

If one power of x or y is one and the other is three it’s a curve with

two bends

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-5 -4 -3 -2 -1 1 2 3 4 5 x

If one power of x or y is one and the other is four it’s a curve with

three bends

-5

-4

-3

-2

-1

1

2

3

4

5 y

y = x4 – 5x3 + 5x2 + 4x – 4

Page 12: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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Draw the graph of the curve y = 2x + 3 from x = – 3 to x = 3

x = – 3 y = 2(– 3) + 3= – 6 + 3 = – 3 (– 3, – 3)

x = – 2 y = 2(– 2) + 3

= – 4 + 3 = – 1 (– 2, – 1)

x = – 1 y = 2(– 1) + 3

= – 2 + 3 = 1 (– 1, 1)

x = 0 y = 2(0) + 3

= 0 + 3 = 3 (0, 3)

y = 2x + 3

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Draw the graph of the curve y = 2x + 3 from x = – 3 to x = 3

x = 1 y = 2(1) + 3= 2 + 3 = 5 (1, 5)

x = 2 y = 2( 2) + 3

= 4 + 3 = 7 ( 2, 7)

x = 3 y = 2(3) + 3

= 6 + 3 = 9 (3, 9)

y = 2x + 3

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-3 -2 -1 1 2 3 x

-4

-3

-2

-1

y

1

2

3

4

5

6

7

8

9

10

y = 2x + 3(– 3, – 3)

(– 2, – 1)

(– 1, 1)

(1, 5)

(2, 7)

(3, 9)

(0, 3)

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Draw the graph of the curve y = x3 – 3x2 – 4x + 12 from x = – 3 to x = 3

x = – 3 y = (– 3)3 – 3(– 3)2 – 4(– 3) + 12 = – 27 – 27 + 12 + 12 = – 30 (– 3, – 30)

x = – 2 y = (– 2)3 – 3(– 2)2 – 4(– 2) + 12

= – 8 – 12 + 8 + 12 = 0 (– 2, 0)

x = – 1 y = (– 1)3 – 3(– 1)2 – 4(– 1) + 12

= – 1 – 3 + 4 + 12 = 12 (– 1, 12)

x = 0 y = (0)3 – 3(0)2 – 4(0) + 12

= 0 – 0 – 0 + 12 = 12 (0, 12)

y = x3 – 3x2 – 4x + 12

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Draw the graph of the curve y = x3 – 3x2 – 4x + 12 from x = – 3 to x = 3

x = 1 y = (1)3 – 3(1)2 – 4(1) + 12 = 1 – 3 – 4 + 12 = 6 (1, 6)

x = 2 y = (2)3 – 3( 2)2 – 4( 2) + 12

= 8 – 12 + 8 + 12 = 0 ( 2, 0)

x = 3 y = (3)3 – 3(3)2 – 4(3) + 12

= 27 – 27 – 12 + 12 = 0 (3, 0)

y = x3 – 3x2 – 4x + 12

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-3 -2 -1 1 2 3 4x

-4

-2

2

4

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12

14

y

y = x3 – 3x2 – 4x + 12

(– 1, 12) (0, 12)

(3, 0)(– 2, 0) (2, 0)

(1, 6)

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Draw the graph of the curve x2 + y2 = 9

(0)2 + y2 = 9

x2 + y2 = 9

y2 = 9x = 0 y = 3

(0, 3) (0, – 3)

x2 + (0)2 = 9 x2 = 9y = 0 x = 3

(3, 0) (– 3, 0)

Page 19: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

x2 + y2 = 9

Circle r = 3

(0, 3)(0, – 3)

(3, 0)

(– 3, 0)

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Draw the graph of the curve y = x4 – 5x3 + 5x2 + 5x – 6 from x = – 2 to x = 3

x = – 2 y = (– 2)4 – 5(– 2)3 + 5(– 2)2 + 5(– 2) – 6

= 16 + 40 + 20 – 10 – 6 = 0 (– 2, 60)

x = – 1 y = (– 1)4 – 5(– 1)3 + 5(– 1)2 + 5(– 1) – 6

= 1 + 5 + 5 – 5 – 6 = 0 (– 1, 0)

x = 0 y = (0)4 – 5(0)3 + 5(0)2 + 5(0) – 6

= 0 – 0 + 0 + 0 – 6 = – 6 (0, – 6)

y = x4 – 5x3 + 5x2 + 5x – 6

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Draw the graph of the curve y = x4 – 5x3 + 5x2 + 5x – 6 from x = – 2 to x = 3

x = 1 y = ( 1)4 – 5(1)3 + 5( 1)2 + 5(1) – 6

= 1 – 5 + 5 – 10 – 6 = 0 (1, 0)

x = 2 y = (2)4 – 5(2)3 + 5(2)2 + 5(2) – 6

= 16 – 40 + 20 + 10 – 6 = 0 (2, 0)

x = 3 y = (3)4 – 5(3)3 + 5(3)2 + 5(3) – 6

= 81 – 135 + 45 + 15 – 6 = 0 (3, 0)

y = x4 – 5x3 + 5x2 + 5x – 6

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-2 -1x

1 2 3 4

-7

-6

-5

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-3

-2

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1

2

3

4

5

y

(0, – 6)

(3, 0)(– 1, 0) (2, 0)(1, 0)

y = x4 – 5x3 + 5x2 + 5x – 6

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y2 = 9x = 0 y = 3

(0, 3) (0, – 3)

x2 = 4y = 0 x = 2

(2, 0) (– 2, 0)

+ = 19

__y2

4__ x2

Draw the graph of the curve + = 19

__y2

4__ x2

=9__y

2

1

=4__x

2

1

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-2 -1 1 2x

-3

-2

-1

1

2

3

y

Ellipse + = 19__y

2

4__ x2

(0, – 3)

(– 2, 0) (2, 0)

(0, 3)

Page 25: Quit 2 Dimensional graphs 3 Dimensional graphs Functions and graphs Graphing functions.

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