Algebra-2

Question Analysis
This question involves finding the maximum value of a reflected and vertically stretched sine function. The main focus is on how the amplitude ( ) and reflection ( ) affect the function’s range.

Key Concept Explanation
The parent sine function has a range of (minimum value = -1, maximum value = 1).
For :
The amplitude scales the range: new range = .
A negative (e.g., ) reflects the graph over the x-axis but does not change the range (since range uses absolute values of the minimum and maximum).

Step-by-Step Solution
1. Identify in : .
2. Calculate the amplitude: .
3. Determine the range: The scaled range is . The reflection (negative