Question

the graph of ( y = cos x ) is transformed to the graph below. which statement about the graph is not correct?

a. the period is ( pi ).
b. the midline is ( y = 1 ).
c. the amplitude is 3.
d. there is no phase shift.

Explanation:

• Period: The distance between two consecutive peaks/troughs. The graph completes 2 cycles in \(2\pi\), so period = \(\pi\) (A is correct).
• Midline: Average of max and min values. Max = 3, min = -1; midline = \(\frac{3 + (-1)}{2} = 1\) (B is correct).
• Amplitude: Half the distance between max and min. \(\frac{3 - (-1)}{2} = 2\) (C is incorrect).
• Phase shift: The graph starts at (0,3) like \(y = \cos x\) (no shift, D is correct).

Answer:

C. The amplitude is 3.