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Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1

a) Graph the five key points of Parent function on the provided grid.

b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=

c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)

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semsee45

Answer:

See explanation below.

Step-by-step explanation:

Given transformed function:

[tex]y=-2 \sin \left[2(x-45^{\circ})\right]+1[/tex]

Part (a)

The parent function of the given function is:  y = sin(x)

The five key points for graphing the parent function are:

  • 3 x-intercepts  →  (0°, 0)  (180°, 0)  (360°, 0)
  • maximum point  →  (90°, 1)
  • minimum point  →  (270°, -1)

(See attachment 1)

Part (b)

Standard form of a sine function:

[tex]\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}[/tex]

where:

  • A = amplitude (height from the mid-line to the peak)
  • 2π/B = period (horizontal distance between consecutive peaks)
  • C = phase shift (horizontal shift - positive is to the left)
  • D = vertical shift (axis of symmetry: y = D)

Therefore, for the given transformed function:

[tex]y=-2 \sin \left[2(x-45^{\circ})\right]+1[/tex]

  • Amplitude = -2
  • Period = 2π/2 = π
  • Phase shift = 45° to the right
  • Equation of axis of symmetry:  y = 1

Part (c)

See attachment 2.

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