Answer:y = 2 * sin(5πx) + 4
Explanation:
To write a sine function with a midline of y = 4, an amplitude of 2, a period of ⅖, and a horizontal shift to the right, we can use the general form of a sine function:
y = A * sin(B(x - C)) + D
where:
- A represents the amplitude
- B determines the period (B = 2π/period)
- C indicates the horizontal shift
- D represents the vertical shift (or midline)
Given the provided information, we can substitute the values:
Amplitude (A) = 2
Period = ⅖ (2/5)
Horizontal shift (C) =?
Vertical shift (D) = 4 (midline)
Now, let's determine the values for B and C:
B = 2π/period = 2π/(2/5) = 5π
Since the question does not specify the exact horizontal shift, we can use any value for C as long as it indicates a shift to the right. Let's choose C = 0 for simplicity.
By substituting the values into the general form of the sine function, we have:
y = 2 * sin(5π(x - 0)) + 4
Simplifying further, we get:
y = 2 * sin(5πx) + 4
Therefore, a sine function with a midline of y = 4, an amplitude of 2, a period of ⅖, and a horizontal shift to the right can be represented by the equation:
y = 2 * sin(5πx) + 4