Starting from a graph of the original function, it's easy to graph a linear coordinate transformation of it. The key principles are these:
More concretely, consider these examples:
Coordinate transformation of f: | Effect on the graph: |
---|---|
f(x) + 3, | Shift 3 units upwards; |
f(x) − 3, | Shift 3 units downwards; |
2f(x), | Stretch vertically by a factor of 2; |
f(x)/2, | Compress vertically by a factor of 2; |
−f(x), | Flip vertically across the horizontal axis; |
−2f(x), | Flip and stretch vertically; |
2f(x) + 3, | Stretch vertically and then shift upwards; |
f(x + 3), | Shift 3 units to the left; |
f(x − 3), | Shift 3 units to the right; |
f(2x), | Compress horizontally by a factor of 2; |
f(x/2), | Stretch horizontally by a factor of 2; |
f(−x), | Flip horizontally across the vertical axis; |
f(−2x), | Flip and compress horizontally; |
f(2x + 3), | Shift to the left and then compress horizontally; |
2f(x + 3), | Stretch vertically and shift to the left, in either order. |
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