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2. 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)

Respuesta :

MrRoyal

The five key points of the parent function are:

  • Domain: Set of all real numbers
  • Range: Set of all real numbers from -1 to 1 (inclusive)
  • No vertical asymptote
  • No horizontal asymptote
  • Maximum: (π/2 + 2πn, 1)

The five key points of the parent function

The function is given as:

y = -2 sin[2(x - 45)] + 1

The above function is a sine function, and the parent function of a sine function is

y = sin(x)

The properties of the above function are:

  • Domain: Set of all real numbers
  • Range: Set of all real numbers from -1 to 1 (inclusive)
  • No vertical asymptote
  • No horizontal asymptote
  • Maximum: (π/2 + 2πn, 1)

The transformed function

The transformed function is given as:

y = -2 sin[2(x - 45)] + 1

A sine function is represented as:

y = A sin[Bx + C] + D

Where:

  • A represents the amplitude
  • Period = 2π/B
  • C represents horizontal phase shift

Using the above representations, we have:

  • Amplitude = -2
  • Period = 2π/2 = π
  • Horizontal phase shift, C = 2 * -45 = -90
  • Equation of the axis, y = 1

The graph of the function

See attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1

Read more about sine functions at:

brainly.com/question/9565966

#SPJ1

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