Question

Which is not a correct description of the graph below?
The graph shows a sine wave with a minimum value of negative 1 and a maximum value of 1. The wave completes 1 cycle in an interval from 0 to 2 pi. The wave passes through (0, 0), slopes down and hits a minimum value of negative 1 at pi over 2, has a value of 0 again at pi, hits a maximum value of 1 at 3 pi over 2 and has a value of 0 again at 2 pi.

the graph of shifted to the left by units

the graph of shifted to the left by units



shifted to the left by units

Answer 1

I can’t tell which choice is wrong unless you paste the exact answer choices. From the graph description the function is y = −sin x (it has period 2π, y(0)=0, slope negative at 0, y(π/2)=−1, y(π)=0, y(3π/2)=1). So any description algebraically equal to −sin x is correct, and any description not equal to −sin x is wrong.

Equivalent correct forms include (among many)
- y = −sin x
- y = sin(x + π) or y = sin(x − π)
- y = sin(−x)
- y = cos(x + π/2)
(you can verify these give y(π/2)=−1, y(π)=0, etc.)

Examples of incorrect descriptions:
- “the graph of sin x shifted left by π/2” (that is y = sin(x + π/2) = cos x) is not correct, because cos(π/2)=0, not −1.
- Any shift of sin x by a value that is not an odd multiple of π will not match the graph.

If you paste the exact choices I will mark which one is not correct and show the quick check.