Question

below is the graph of a trigonometric function. it has a minimum point at \\((2, -0.9)\\) and an amplitude of 3.

what is the midline equation of the function?

\\(y = \\)

Explanation:

Identify given values

The minimum value is \(y_{\text{min}} = -0.9\).
The amplitude is \(A = 3\).

Relate midline to minimum and amplitude

Using the Amplitude and Minimum concept:
The midline \(y = d\) lies exactly one amplitude above the minimum value.

$$d = y_{\text{min}} + A$$

Calculate the midline value

Using the Trigonometric Midline concept:

$$d = -0.9 + 3 = 2.1$$

Thus, the equation of the midline is \(y = 2.1\).

Answer:

What is the midline equation of the function?

\(y =\) <blank>2.1</blank>