Understanding Sine Function Transformations

The video tutorial explains how to analyze a given sine function by identifying its vertical shift, midline, amplitude, period, and phase shift. The function is rewritten in a standard form to easily determine the parameters a, b, c, and d. The vertical shift and midline are calculated based on the value of c, while the amplitude is derived from the absolute value of a. The period is calculated using the formula 2π/b, and the phase shift is determined by the value of d. The tutorial concludes with a graph verification to ensure the calculations are correct.

What is the first step in finding the vertical shift, midline, amplitude, period, and phase shift of a sine function?

• Identify the maximum and minimum values.

• Rewrite the function in a specific form.

• Graph the function directly.

• Calculate the derivative of the function.

When rewriting the sine function, what is factored out from the binomial?

• 11 pi over six

• 5 pi

• 2 pi

• 6 pi

How is the vertical shift of a sine function determined?

• By the value of a

• By the value of b

• By the value of c

• By the value of d

What effect does a negative value of 'a' have on the graph of a sine function?

• It increases the amplitude.

• It reflects the graph across the midline.

• It shifts the graph upwards.

• It changes the period.

How is the period of a sine function calculated?

• By dividing 2 pi by the value of b

• By multiplying the amplitude by 2

• By subtracting the vertical shift from 2 pi

• By adding the phase shift to 2 pi

What does a negative value of 'd' indicate about the phase shift?

• The function is shifted downwards.

• The function is shifted upwards.

• The function is shifted to the left.

• The function is shifted to the right.

What is the starting point for graphing one period of the given sine function?

• x equals negative five

• x equals positive five

• x equals negative three

• x equals zero

How is the maximum function value determined for the given sine function?

• By adding the amplitude to the midline

• By multiplying the amplitude by the period

• By dividing the amplitude by the period

• By subtracting the amplitude from the midline

What is the pattern used to graph the basic sine function over one period?

• Minimum, midline, maximum, midline

• Midline, minimum, midline, maximum

• Midline, maximum, midline, minimum

• Maximum, midline, minimum, midline

What is the purpose of verifying the results by graphing the function?

• To check the accuracy of the calculated values

• To find the derivative of the function

• To determine the function's domain

• To calculate the function's range