11 X1 T02 10 shifting curves II
-
Upload
nigel-simmons -
Category
Education
-
view
273 -
download
0
Transcript of 11 X1 T02 10 shifting curves II
![Page 1: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/1.jpg)
Shifting Curves II
![Page 2: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/2.jpg)
Shifting Curves II y kf x 1, curve is steeperk
0 1, curve is shallowerk (curve is stretched vertically)
ORy f xk
![Page 3: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/3.jpg)
Shifting Curves II y kf x 1, curve is steeperk
0 1, curve is shallowerk (curve is stretched vertically)domain unchanged, range altered
ORy f xk
![Page 4: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/4.jpg)
Shifting Curves II y kf x 1, curve is steeperk
0 1, curve is shallowerk (curve is stretched vertically)domain unchanged, range altered
y f kx 1, curve is steeperk 0 1, curve is shallowerk (curve is stretched horizontally)
ORy f xk
![Page 5: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/5.jpg)
Shifting Curves II y kf x 1, curve is steeperk
0 1, curve is shallowerk (curve is stretched vertically)domain unchanged, range altered
y f kx 1, curve is steeperk 0 1, curve is shallowerk (curve is stretched horizontally)domain altered, range unchanged
ORy f xk
![Page 6: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/6.jpg)
Shifting Curves II y kf x 1, curve is steeperk
1y
f x intercepts asymptotesx
0 1, curve is shallowerk (curve is stretched vertically)domain unchanged, range altered
y f kx 1, curve is steeperk 0 1, curve is shallowerk (curve is stretched horizontally)domain altered, range unchanged
asymptotes interceptsx1 1y y 1 1y y
ORy f xk
![Page 7: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/7.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x
![Page 8: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/8.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
![Page 9: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/9.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x
![Page 10: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/10.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x 22y x
![Page 11: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/11.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x
212
y x
![Page 12: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/12.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x
212
y x
22y x
![Page 13: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/13.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x
212
y x
22y x
22( ) Sketch 1
4yii x
![Page 14: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/14.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x
212
y x
22y x
22( ) Sketch 1
4yii x y
x
2 21. : 1basic curve x y
1
1
–1
–1
![Page 15: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/15.jpg)
y
x
e.g. on one graph drawi1) , , 22
a y x y x y x
y x12
y x
2y x2 2 21) , , 2
2b y x y x y x
y
x
2y x
212
y x
22y x
22( ) Sketch 1
4yii x y
x
2 21. : 1basic curve x y
1
1
–1
–1
22
2. , 24 2y y k
stretch vertically by a factor of 2
![Page 16: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/16.jpg)
21
2iii y
x
![Page 17: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/17.jpg)
y
x
21. : basic curve y x
21
2iii y
x
![Page 18: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/18.jpg)
y
x
21. : basic curve y x
21
2iii y
x
2. reflect in x axis
![Page 19: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/19.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis
2
![Page 20: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/20.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis2
4. x intercepts become asymptotes
22
![Page 21: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/21.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis2
4. x intercepts become asymptotes
22
5. y >1 become y <112
![Page 22: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/22.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis2
4. x intercepts become asymptotes
22
5. y >1 become y <112
6. y <1 become y >1
![Page 23: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/23.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis2
4. x intercepts become asymptotes
22
5. y >1 become y <112
6. y <1 become y >1
![Page 24: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/24.jpg)
y
x
21. : basic curve y x
21
2iii y
x
3. shift up 2 units
2. reflect in x axis2
4. x intercepts become asymptotes
22
5. y >1 become y <112
6. y <1 become y >1
![Page 25: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/25.jpg)
1iv y xx
![Page 26: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/26.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
![Page 27: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/27.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
![Page 28: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/28.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
- points of intersection
![Page 29: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/29.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
- points of intersection - as many other points as youneed to work out the shape
![Page 30: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/30.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
- points of intersection - as many other points as youneed to work out the shape
![Page 31: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/31.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
- points of intersection - as many other points as youneed to work out the shape
![Page 32: 11 X1 T02 10 shifting curves II](https://reader033.fdocuments.us/reader033/viewer/2022052907/55925bfd1a28ab1b098b457e/html5/thumbnails/32.jpg)
1iv y xx
y
x
1. :1 and
draw the basic curves
y x yx
2. add the y values together* choose key points first
- x interceptsnote: vertical asymptotes remain
- points of intersection - as many other points as youneed to work out the shape
Exercise 2J: 1, 2a, 3b, 4c, 5ac, 6b, 7ac, 8, 9