M3B 3.08 Sinusoidal Graphs

​M3B: 3.08 Sinusoidal Graphs

Today we're going to learn about the sine function as a graph, and determine some of the key features of these graphs.

Hotspot

Select all points that could be used to find the "maximum value" of the graphed function.

Multiple Choice

What is the maximum of the function graphed?

• 5

• -1

• 2

• 3

Hotspot

Select all points that could be used to find the "minimum value" of the graphed function.

Drag and Drop

What are the maximum and minimum values of the graphed function?

maximum: ​

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minimum: ​

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Drag these tiles and drop them in the correct blank above

3

-3

0

-2

-4

4

1

2

-1

Multiple Select

Which of the following functions have a minimum value of 1? Select all that apply.

Multiple Choice

What is the equation of the midline of the graph?

• y = -3

• y = 2

• y = -2

• y = 3

Multiple Choice

What is the midline of the graphed function above?

• y = 2

• y = 0

• y = 5

• y = 3

Hotspot

At what height would you place the midline of this graphed function?

Multiple Choice

What is the midline of the function graphed?

• y = -3

• y = 3

• y = 0

• y = -6

Fill in the Blanks

Match

Match each graphed function to the equation of its midline.

y = 3

y = 0

y = 4

y = 2

• y = 3

• y = 0

• y = 4

• y = 2

Multiple Choice

What is the amplitude of the graph?

• -3

• 2

• -2

• 3

Multiple Choice

What is the amplitude in the function graphed above?

• -5

• 5

• 4

• 0

Fill in the Blanks

Match

Match each graphed function to its amplitude.

4

2

3

1

• 4

• 2

• 3

• 1

Fill in the Blanks

Reorder

Put the graphs in order from smallest to largest by amplitude.

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

What is the period of the graphed function?

• π/2

• π

• 2π

• 5π/2

Multiple Choice

What is the period in the graphed function?

• 2π

• 4π

• π

• π/2

Multiple Choice

What is the period of the function graphed?

• π/2

• π

• 3π/2

• 2π

Multiple Choice

What is the period of the function graphed?

• π/2

• π

• 3π/2

• 2π

Multiple Choice

What is the period of the function graphed?

• π

• 2π

• π/2

• 3π/2

Multiple Choice

What is the amplitude of the graphed function above?

• 2

• 0

• 5

• 3

Multiple Choice

What is the period of the graphed function?

• π/4

• 2π

• π/2

• π

Multiple Choice

What is the period of the function graphed above?

• 5π/2

• 2π

• π

• 3π

Drag and Drop

Describe the features of the graphed function:

min: ​

Placeholder

max:

Placeholder

midline: y = ​

Placeholder

amplitude: ​

Placeholder

period: ​

Placeholder

Drag these tiles and drop them in the correct blank above

1

3

2

4

-3

6

Multiple Choice

Which graph correctly highlights a single cycle for sine, which could be useful in finding the period of the function?

Multiple Choice

What is the equation of the midline of the graph?

• y = -1

• y = 0

• y = 3

• y = -3

Multiple Choice

Which of the following statements CORRECTLY describes the graphed function?

• The amplitude is 1 unit.

• The period is 9π/2.

• The equation of the midline is y = 2.

• The maximum value is 3.

Multiple Choice

Which graphed function has the larger amplitude, f(x) or g(x)?

• f(x) has the larger amplitude.

• g(x) has the larger amplitude.

• Both functions have the same amplitude.

Multiple Choice

What is the difference between the amplitude of g(x) and the amplitude of f(x)?

• 2

• 4

• 5

• 8

Multiple Choice

What is the difference between the maximum value of f(x) and the minimum value of g(x)?

• 11

• 3

• 7

• 13

Multiple Choice

Which line correctly represents the midline of the graphed function?

Multiple Choice

Which graphed function has a higher maximum value, f(x) or g(x)?

• f(x) has the higher maximum value.

• g(x) has the higher maximum value.

• Both functions have the same maximum value.

Match

Match each function to its period.

4π

π

π/2

• 4π

• π

• π/2

Multiple Choice

Which line correctly represents the amplitude of the graphed function?

Categorize

Options (5)

The maximum value is 6.

The minimum value is -5.

The amplitude of the function is 3.

The midline is located at y = 2.

The period of the function is 2π.

Determine whether each statement is CORRECT or INCORRECT for the graphed function. (Click on the picture icon to enlarge the graph!)

CORRECT

INCORRECT

Match

Match each function to a correct statement about is features.

Has an amplitude of 4 units.

Has a minimum value of -2.

Has a period of π.

Has a midline at y = 2.

• Has an amplitude of 4 units.

• Has a minimum value of -2.

• Has a period of π.

• Has a midline at y = 2.