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:
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