How do you determine the period of a sine function given in the form $$f(x) = A \times \text{sin}(Bx + C) + D$$ ?

The period can be determined using the formula: Period = $$\frac{2\theta}{|B|}$$ .

What transformation is applied to the graph of $$f(x) = \text{sin}(x)$$ to obtain $$f(x) = \text{sin}(x - \frac{\theta}{2})$$ ?

This transformation is a horizontal shift (phase shift) to the right by $$\frac{\theta}{2}$$ .

How can you identify a periodic function from its graph?

A graph is periodic if it shows a repeating pattern over a specific interval.

What is the effect of changing the value of A in the function $$f(x) = A \times \text{sin}(x)$$ ?

Changing the value of A affects the amplitude of the sine wave. A larger |A| results in a taller wave.

What is the effect of changing the value of B in the function $$f(x) = \text{sin}(Bx)$$ ?

Changing the value of B affects the period of the sine wave. The period is given by $$\frac{2\theta}{|B|}$$ .

What does the term 'midline' refer to in periodic functions?

The midline is the horizontal line that runs through the middle of the graph of a periodic function, representing the average value of the function.

What is the difference between even and odd functions in terms of symmetry?

Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.

What is the transformation applied to the graph of $$f(x) = \text{cos}(x)$$ to obtain $$f(x) = \text{cos}(x + \frac{\theta}{2})$$ ?

This transformation is a horizontal shift (phase shift) to the left by $$\frac{\theta}{2}$$ .

How do you find the vertical shift of a periodic function?

The vertical shift is determined by the constant D in the function form $$f(x) = A \times \text{sin}(Bx + C) + D$$ , which moves the graph up or down.

What is the relationship between the sine and cosine functions?

The sine and cosine functions are phase-shifted versions of each other, with $$\text{sin}(x) = \text{cos}(x - \frac{\theta}{2})$$ .

Periodic Functions and Transformations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a periodic function?

Back

Tags

CCSS.HSF.TF.A.4

2.

FLASHCARD QUESTION

Front

What is the period of a function?

Back

Tags

CCSS.HSF.TF.A.4

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.4

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

What does a reflection across the x-axis do to the graph of a function?

Back

Tags

CCSS.HSF.BF.B.3

6.

FLASHCARD QUESTION

Front

What is the amplitude of a periodic function?

Back

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

What is a phase shift in periodic functions?

Back

A phase shift is a horizontal shift of the graph of a function. It occurs when the input variable is adjusted by a constant.

Tags

CCSS.HSF-IF.C.7E

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