13b graf intro
TRANSCRIPT
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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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Tuesday, January 27, 2015