Questions: Identify the transformations for the following transformed cos function that is reflected over the x axis: Period = Choose... Vertical Shift = Choose... Amplitude = Choose... Phase Shift = Choose...

Solution Steps

The period of a cosine function is the length of one complete cycle. For the standard cosine function, \( \cos(x) \), the period is \( 2\pi \). In the given graph, one complete cycle also spans from \( 0 \) to \( 2\pi \), so the period remains \( 2\pi \).

The vertical shift is the amount by which the graph is shifted up or down. The standard cosine function oscillates between 1 and -1. In the given graph, the function oscillates between 2 and -2, indicating no vertical shift.

The amplitude is the distance from the midline to the maximum or minimum value of the function. For the standard cosine function, the amplitude is 1. In the given graph, the amplitude is 2, as the function oscillates between 2 and -2.

The phase shift is the horizontal shift of the graph. The standard cosine function starts at its maximum value at \( x = 0 \). In the given graph, the function also starts at its maximum value at \( x = 0 \), indicating no phase shift.

Final Answer