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Functions
Pre-Calc: Shifts, Reflections, Stretching, and Shrinking
| Term | Definition |
|---|---|
| y = f(x) + c | Raise the graph by c units |
| y = f(x) - c | Lower the graph by c units |
| y = f(x+c) | Shift the graph of f to the left c units |
| y = f(x-c) | Shift the graph to the right c units |
| y = -f(x) | Reflect the graph about the x axis |
| y = f(-x) | Reflect the graph of f about the y-axis |
| y = cf(x), c > 1 | Multiply each y-coordinate of y = f(x) by c, vertically stretching the graph of f |
| y = cf(x), 0 < c < 1 | Multiply each y-coordinate of y = f(x) by c, vertically shrinking the graph of f |
| y = f(cx), c >1 | Divide each x-coordinate of y = f(x) by c, horizontally shrinking the graph of f |
| y = f(cx), 0 < c < 1 | Divide each x-coordinate of y = f(x) by c, horizontally stretching the graph of f |