Periodic Functions and Transformations

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What is a periodic function?

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A periodic function is a function that repeats its values at regular intervals or periods. For example, the sine and cosine functions are periodic with a period of 2π.

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CCSS.HSF.TF.A.4

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What is the amplitude of a periodic function?

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The amplitude of a periodic function is the maximum distance from the midline (equilibrium position) to the peak (or trough) of the wave. It represents the height of the wave.

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CCSS.HSF-IF.C.7E

Front

What transformation occurs when a function is reflected across the x-axis?

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CCSS.HSF.BF.B.3

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How can you identify a periodic function from its graph?

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A periodic function will show a repeating pattern in its graph. The intervals between peaks and troughs will be consistent.

Tags

CCSS.HSF.TF.A.4

Front

What is the period of the sine function?

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The period of the sine function is 2π, meaning it completes one full cycle every 2π units along the x-axis.

Tags

CCSS.HSF.TF.A.4

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What is the difference between sine and cosine functions?

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Sine and cosine functions are both periodic, but they are phase-shifted by π/2. The sine function starts at 0, while the cosine function starts at its maximum value.

Tags

CCSS.HSF-IF.C.7E

Front

What is a transformation in the context of functions?

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A transformation is an operation that alters the position, size, or shape of a graph. Common transformations include translations, reflections, stretches, and compressions.

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CCSS.HSF.BF.B.3

Front

What does it mean to translate a function vertically?

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CCSS.HSF-IF.C.7E

Front

What is the effect of a horizontal stretch on a periodic function?

Back

Tags

CCSS.HSF-IF.C.7E

Front

What is the equation of a cosine function with an amplitude of 2 and a vertical shift of -1?

Back

Tags

CCSS.HSF-IF.C.7E