13b Graf Intro

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    AIRIL AHMAD

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    Graph of Functions

    EN.AIRIL BIN AHMAD

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    Graph

    Functions

    y = 2x2

    -5

    y = x + 3 y = x3+ 4

    6 4 2 2 4 6

    4

    3

    2

    1

    1

    x

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    Exampe 1!"#$en %&e 'un(%#)n, y* x+ . -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 1(m %) 1un#% )n yax#s.

    3 2 1 0 1 2 3

    4

    When x= - 4: y= - 4+ 3 = -1

    When x= -3: y= -3+ 3 = 0

    When x= -2: y= -2+ 3 = 1

    When x= -1: y= -1+ 3 = 2

    When x= 0: y= 0+3 = 3

    When x= 1: y= 1+3 = 4

    When x= 2: y= 2+3 = 5

    When x= 3: y= 3+3 = 6

    When x= 4: y= 4+3 = 7

    1 0 1 2 3 5 7

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    2(m

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    2(m

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    !

    2c" to 1 unit on x-axis1c" to 1unit on y-axis

    1 2-1-2 0

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    !

    1c" to 1unit on y-axis

    1 2-1-2 0

    1

    2

    -1

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    Exampe 1!"#$en %&e 'un(%#)n, y* x+ . -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 1(m %) 1un#% )n yax#s.

    3 2 1 0 1 2 3

    4

    When x= - 4: y= - 4+ 3 = -1

    When x= -3: y= -3+ 3 = 0

    When x= -2: y= -2+ 3 = 1

    When x= -1: y= -1+ 3 = 2

    When x= 0: y= 0+3 = 3

    When x= 1: y= 1+3 = 4

    When x= 2: y= 2+3 = 5

    When x= 3: y= 3+3 = 6

    When x= 4: y= 4+3 = 7

    1 0 1 2 3 5 7

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    !

    1 2-1-2 0

    1

    2

    -1

    ! -2

    1

    -1

    2

    y=x+

    3

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    3 2 1 0 1 2 3

    4

    When x=-4: y= 2x#-4$+ 1 =-7

    When x=-3: y= 2x#-3$+ 1 = -5

    When x=-2: y= 2x#-2$+ 1 = -3

    When x=-1: y= 2x#-1$+ 1 = -1

    When x= 0: y= 2x#0$+ 1 = 1

    When x= 1: y= 2x#1$+ 1 = 3

    When x= 2: y= 2x#2$+ 1 = 5

    When x= 3: y= 2x#3$+ 1 = 7

    When x= 4: y= 2x#4$+ 1 = %

    7 5 1 1 5 7 6

    Exampe 2!"#$en %&e 'un(%#)n, y* 2x+ 1. -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n 2(m %) 1 un#% )n xax#s and 1(m %) 1un#% )n yax#s.

    3

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    Red Eua%#)n ! y*x+Bue Eua%#)n ! y*2x+1

    4

    3

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    3 2 1 0 1 2 3

    4 13 10 2 2 10 13 18

    Exampe !

    "#$en %&e 'un(%#)n, y* 3x 2. -)py and ()mpe%e %&e %ae. Dra/ a rap&ased )n %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 1(m %) 2 un#%s )n yax#s.

    3 2 1 0 1 2 3

    4

    Exampe 3!

    "#$en %&e 'un(%#)n, y* 2x+ 2. -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n %&e da%a /#%&2(m %) 1 un#% )n xax#s and 1(m %) 2 un#%s )n yax#s.

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    Red eua%#)ns ! y* 3x2

    Bue eua%#)ns! y* 2x+3

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    3 2 1 0 1 2 3

    4 12 5 0 3 0 5 12

    Exampe 5!

    "#$en %&e 'un(%#)n, y* x2 3. -)py and ()mpe%e %&e %ae. Dra/ a rap&ased )n %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 1(m %) 2 un#%s )n yax#s.

    3 2 1 0 1 2 3

    4 3 8 11 12 11 8 3

    Exampe !

    "#$en %&e 'un(%#)n, y* 12 x2. -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n the &ata 'ith2(m %) 1 un#% )n xax#s and 1(m %) 2un#%s )n yax#s.

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    2

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    Red Eua%#)n ! y* x9+2

    Bue Eua%#)n ! y* x9

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    2 1 0 1 2

    4

    Exampe 7!

    "#$en %&e 'un(%#)n, y* x 2. -)py and ()mpe%e %&e %ae. Dra/ a rap&ased )n %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 2(m %) 5 un#%s )n yax#s.

    2 1 0 1 2

    4

    Exampe 8!

    "#$en %&e 'un(%#)n, y* 10 :x. -)py and ()mpe%e %&e %ae. Dra/ a rap&

    ased )n the &ata 'ith2(m %) 1 un#% )n xax#s and 2 (m %) 5 un#%s )n yax#s.

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    4 3 2 1 1 2 3 4

    Red Eua%#)n ! y* x;+2

    Bue Eua%#)n ! y* 10 x;

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    2 1 0 1 2

    4 8 13 0 3 23

    Exampe 6!

    "#$en %&e 'un(%#)n, y* 3x22x. -)py %&e %ae and dra/ a rap& ased )n

    %&e da%a /#%& 2(m %) 1 un#% )n xax#s and 2(m %) 5 un#%s )n yax#s.

    =r)m %&e rap&, '#nd %&e $aue )' y /&en!

    a. * 2 . x* 2.2 (. x* 2.5 d. x* 1.5

    =r)m %&e rap&, '#nd %&e $aue )' x /&en!

    e. y* 10 '. y* 20 . y* 5 &. 4 * 15

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