- 1). Shift the graph of a function up or down by adding or subtracting to a function. The general expression for shifting a function upward is f(x) + a. The general expression for shifting a function downward is f(x) - a. Where "a" is any constant number the function is shifted "a" units up or down.
- 2). Shift the graph of a function left or right by adding or subtracting to the x-variable of the function. The general expression for shifting a function leftward is f(x + a). The general expression for shifting a function rightward is f(x- a). Where "a" is any constant number the function is shifted "a" units to the right or left.
- 3). Reflect the graph of a function about the x-axis (flip it upside down) by making the function negative. The general expression for reflecting the graph of a function about the x-axis is -f(x).
- 4). Reflect the graph of a function about the y-axis (its mirror image) by making the x-variable of the function negative. The general expression for reflecting the graph of a function about the y-axis is f(-x).
- 5). Steepen or flatten the graph of a function by multiplying x-variable by a number "a." If "a" is an integer the graph will become steeper because the function grows faster. If "a" is a fraction the function will flatten as the function grows more slowly.
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