A sine function has the following key features:

Frequency = 14π

Amplitude = 2

Mid-line: y = 2

y-intercept: (0, 2)

The function is not a reflection of its parent function over the x-axis.

The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.

To find the equation of the sine function given the provided key features, you can use the general form of the sine function:

y = A*sin(Bx + C) + D

Here's how you can determine the values for A, B, C, and D using the given information:

1. Amplitude (A): Given as 2, which represents the vertical distance between the maximum and minimum values of the function.

2. Frequency (B): Given as 14π, which represents the number of cycles completed in a period of 2π. Since the standard period of the sine function is 2π, the frequency can be calculated as B = 2π/period. In this case, the period is 14π, so B = 2π/(14π) = 1/7.

3. Mid-line (D): Given as y = 2, which represents the horizontal line where the sine function oscillates around. It is also the average value of the function. Therefore, D = 2.

4. Phase shift (C): The function is not a reflection of its parent function over the x-axis, so C = 0. The phase shift is determined when the function is shifted horizontally.

With these values, the equation of the sine function can be written as:

y = 2*sin((1/7)x) + 2

This equation satisfies all the given key features.

The y-intercept is given as (0, 2), which means the value of y when x = 0 is 2. This confirms that the constant term (D) is indeed 2, as calculated earlier.

Remember, when solving problems like this, it's crucial to understand the relationship between different key features of the function and how they affect its equation.

so, after all the others whose solution you have seen, what bothers you about this one?