could someone pls help?
what transformations must be applied to the graph of y=sinx to obtain the graph of y=sin(x+150 degrees) + 3. state domain for one cycle and state the range.
Create one equation that shows a function that is translated, stretched, and reflected. After writing your equation, use complete sentences to explain each of the transformations shown in your equation.
Of course, I can help you with that!
To obtain the graph of y = sin(x + 150 degrees) + 3 from the graph of y = sin(x), we need to apply two transformations:
1. Horizontal shift: We need to shift the graph of y = sin(x) 150 degrees to the left.
2. Vertical shift: We need to shift the graph of y = sin(x) 3 units up.
Now let's break down these transformations step by step:
1. Horizontal shift by 150 degrees:
To shift the graph 150 degrees to the left, we need to subtract 150 from the angle inside the sine function. Therefore, the transformation for the horizontal shift is x + 150 degrees.
2. Vertical shift by 3 units up:
To shift the graph 3 units up, we add 3 to the entire function. Therefore, the transformation for the vertical shift is sin(x + 150 degrees) + 3.
Now, let's discuss the domain and range of the transformed function:
Domain:
The domain of both y = sin(x) and y = sin(x + 150 degrees) remains the same, which is all real numbers. Therefore, the domain for one cycle is (-∞, +∞).
Range:
For the function y = sin(x), the range is between -1 and 1. However, when we shift the graph vertically up by 3 units, the range will also shift upwards. So, the range for y = sin(x + 150 degrees) + 3 will be between 2 and 4.
In summary:
The transformations applied to the graph of y = sin(x) to obtain the graph of y = sin(x + 150 degrees) + 3 are a horizontal shift of 150 degrees to the left and a vertical shift of 3 units up. The domain remains the same as (-∞, +∞), and the range is shifted to be between 2 and 4.