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UNIT
2 : FUNCTIONS & TRANSFORMATIONS
LESSON 7:
COMBINATIONS OF TRANSFORMATIONS
|
x |
|
|
0 |
0 |
|
1 |
1 |
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4 |
2 |
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9 |
3 |
|
x |
|
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-4 |
-1/4 |
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-3 |
-1/3 |
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-2 |
-1/2 |
|
-1 |
-1 |
|
-1/2 |
-2 |
|
-1/3 |
-3 |
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-1/4 |
-4 |
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0 |
0 |
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1/4 |
4 |
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1/3 |
3 |
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1/2 |
2 |
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1 |
1 |
|
2 |
1/2 |
|
3 |
1/3 |
|
4 |
1/4 |
![Text Box: In summary, to graph y = af [k(x – m)] + n from the graph of y = f(x), follow these ideas:
· If a < 0, we have a reflection in the x-axis
· If k < 0, we have a reflection in the y-axis
· If –1 < a < 1, we have a vertical compression
· If a > 1 or a < - 1, we have a vertical stretch
· If –1 < k < 1, we have a horizontal stretch, factor 1/k
· If k > 1 or k < - 1, we have a horizontal compression, factor 1/k
· The value of m gives the horizontal translation (shift)
· The value of n gives the vertical translation (shift)](./combinations_files/image045.gif)