What is the vertical and horizontal translation for the function:
y=4sin(4.5x - π) + 3
y=4sin(4.5x - π) + 3
y=4sin(4.5(x - π/4.5) + 3
the sine curve y = 4sin (4.5x) has been moved π/4.5 units to the right and 3 units up
https://www.wolframalpha.com/input/?i=graph+y+%3D+4sin+%284.5x%29+%2C+y+%3D+4sin%284.5x+-+%CF%80%29+%2B+3
To determine the vertical and horizontal translations of a function, we need to know the general form of the function. In this case, the function is in the form: y = A*sin(Bx - C) + D.
In this form, A determines the amplitude (or vertical stretch/compression) of the function, B determines the horizontal stretch/compression, C determines the horizontal translation, and D determines the vertical translation.
Based on the given equation: y = 4sin(4.5x - π) + 3, we can identify the A, B, C, and D values.
1. Amplitude (A): The coefficient in front of the sine function, 4, represents the amplitude. So the amplitude of the function is 4.
2. Horizontal Stretch/Compression (B): The coefficient inside the sine function, 4.5, determines the horizontal stretch or compression. In this case, the horizontal stretch/compression factor is given by 2π/B. So the horizontal stretch/compression is 2π/4.5.
3. Horizontal Translation (-C/B): The term inside the sine function, 4.5x - π, represents the horizontal translation. The horizontal translation is given by -C/B. In this case, -C/B is -(-π)/4.5, which simplifies to π/4.5.
4. Vertical Translation (D): The constant added to the sine function, 3, represents the vertical translation. Therefore, the vertical translation is 3.
So, for the given function, y = 4sin(4.5x - π) + 3:
- The amplitude is 4
- The horizontal stretch/compression factor is 2π/4.5
- The horizontal translation is π/4.5
- The vertical translation is 3.