Question

Consider the function f(x) = 2 sin (?/4 (x - 3)) + 6. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values. Enter the exact answers. Amplitude: A = Period: P = Midline: y = The phase shift is . The vertical translation is . Hints for the maximum and minimum values of f(x): • The maximum value of y = sin (x) is y = 1 and the corresponding x values are x = ?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = ?/2. • The minimum value of y = sin (x) is y = -1 and the corresponding x values are x = 3?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = 3?/2. • If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles. • If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles. For x in the interval [0, P], the maximum y-value and corresponding x-value is at: x = y = For x in the interval [0, P], the minimum y-value and corresponding x-value is at: x = y =

          Consider the function f(x) = 2 sin (?/4 (x - 3)) + 6. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.

Enter the exact answers.

Amplitude: A =
Period: P =
Midline: y =
The phase shift is .
The vertical translation is .

Hints for the maximum and minimum values of f(x):
• The maximum value of y = sin (x) is y = 1 and the corresponding x values are x = ?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = ?/2.
• The minimum value of y = sin (x) is y = -1 and the corresponding x values are x = 3?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = 3?/2.
• If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
• If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.

For x in the interval [0, P], the maximum y-value and corresponding x-value is at:

x =
y =

For x in the interval [0, P], the minimum y-value and corresponding x-value is at:

x =
y =

Consider the function f(x) = 2 sin (?/4 (x - 3)) + 6. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.

Enter the exact answers.

Amplitude: A =
Period: P =
Midline: y =
The phase shift is .
The vertical translation is .

Hints for the maximum and minimum values of f(x):
• The maximum value of y = sin (x) is y = 1 and the corresponding x values are x = ?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = ?/2.
• The minimum value of y = sin (x) is y = -1 and the corresponding x values are x = 3?/2 and multiples of 2? less than than and more than this x value. You may want to solve (?/4)(x - 3) = 3?/2.
• If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
• If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.

For x in the interval [0, P], the maximum y-value and corresponding x-value is at:

x =
y =

For x in the interval [0, P], the minimum y-value and corresponding x-value is at:

x =
y =

Added by Lisa B.

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