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Trigonometric Function Transformations
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Vertical shift
Shifts the graph up or down without altering its shape.
Horizontal shift
Shifts the graph to the left or right without altering its shape.
Vertical stretch
Stretches or compresses the graph vertically, affecting the amplitude.
Horizontal stretch
Stretches or compresses the graph horizontally, affecting the period.
Reflection across the x-axis
Flips the graph over the x-axis, reversing the sign of the outputs.
Reflection across the y-axis
Flips the graph over the y-axis, altering the function's progression over the x-axis.
Period change
Alters the length of one complete cycle of the graph.
Amplitude change
Adjusts the distance from the midline to the peak (or trough) of the graph.
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