Ask a New Question
Menu

Ms. Arrowood and Mrs. Owen both described the graph of the function y = sin x − 3 .

ms arrowood says the graph is the sin graph shifted right 3 units . and Mrs owen I think the sin graph is shifted down three units, which one is correct ? and how do you know who is correct ?

1 answer

To determine which description of the function \( y = \sin x - 3 \) is correct, let’s analyze the function step by step.

  1. Understand the basic sine function: The function \( y = \sin x \) oscillates between -1 and 1 with a period of \( 2\pi \).

  2. Identify the transformation: The expression \( y = \sin x - 3 \) indicates a vertical transformation, specifically a vertical shift.

  3. Shifting the sine function:

    • Subtracting \( 3 \) from \( \sin x \) means that every point on the sine graph is shifted down by 3 units.
    • Therefore, instead of oscillating between -1 and 1, the new function \( y = \sin x - 3 \) will oscillate between -4 and -2.

So, Mrs. Owen is correct: the graph of the function is the sine graph shifted down 3 units.

Ms. Arrowood’s statement about the graph being shifted right 3 units is incorrect, as there is no horizontal transformation (right or left shift) indicated in the function \( y = \sin x - 3 \).

In summary, \( y = \sin x - 3 \) represents a vertical shift down by 3 units, confirming Mrs. Owen's statement.