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UNIT
2 : FUNCTIONS & TRANSFORMATIONS
LESSON 7: COMBINATIONS
OF TRANSFORMATIONS HOMEWORK QUESTIONS
![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) [use opposite sign]
· The value of n gives the vertical translation (shift)](./combinationshw_files/image002.gif)
(a)
(b)
(c)
Solutions:
|
x |
|
|
-3 |
-3 |
|
-2 |
-2 |
|
-1 |
-1 |
|
0 |
0 |
|
1 |
1 |
|
2 |
2 |
|
3 |
3 |
|
x |
|
|
0 |
0 |
|
1 |
1 |
|
4 |
2 |
|
9 |
3 |
First sketch the graph of y = 1/x as below.
|
x |
|
|
-3 |
-1/3 |
|
-2 |
-1/2 |
|
-1 |
-1 |
|
-1/2 |
-2 |
|
-1/3 |
-3 |
|
0 |
undefined |
|
1/3 |
3 |
|
1/2 |
2 |
|
1 |
1 |
|
2 |
1/2 |
|
3 |
1/3 |
