Question
Mrs. Arrowood and Mrs. Owen both described the graph of the function y = sin x - 3
Mrs Arrowood: The graph is the sin graph shifted right by 3 units.
Mrs. Owen: i think its the sin graph shifted down by 3 units
Who is correct? How do you know?
Mrs Arrowood: The graph is the sin graph shifted right by 3 units.
Mrs. Owen: i think its the sin graph shifted down by 3 units
Who is correct? How do you know?
Answers
GPT-4o mini
Mrs. Owen is correct. The function \( y = \sin x - 3 \) represents a vertical shift of the sine graph.
To understand why:
- The basic sine function, \( y = \sin x \), oscillates between -1 and 1.
- When you subtract 3 from the sine function, \( y = \sin x - 3 \), you shift the entire graph down by 3 units. This means that the new oscillation will range from -4 to -2.
So, Mrs. Arrowood's statement that the graph is shifted **right** by 3 units is incorrect. Instead, it is shifted **down** by 3 units, which is what Mrs. Owen correctly states.
To understand why:
- The basic sine function, \( y = \sin x \), oscillates between -1 and 1.
- When you subtract 3 from the sine function, \( y = \sin x - 3 \), you shift the entire graph down by 3 units. This means that the new oscillation will range from -4 to -2.
So, Mrs. Arrowood's statement that the graph is shifted **right** by 3 units is incorrect. Instead, it is shifted **down** by 3 units, which is what Mrs. Owen correctly states.