MAT 112 Quiz #2 Remarks

Section 5.4 15-22 (2pts)

1. Describe the relationship between the graphs of f and g.

f(x) = cos (4x -p /2), g(x) = -2 + cos (4x -p /2).

Solution: g(x) is f(x) shifted down 2 units.

Section 5.4 43-60 (8pts)

2. Analyze the graph of g(x) = -2 + 3cos (4x -p /2). Use two decimal accuracy or exact answers.

Solution:

Amplitude = |a| = 3

Period = 2p /b = 2p /4 = 2p (1/4) = p /2

Phase shift = c/b = p /2/4 = p /2 (1/4) = p /8

Vertical translation = d = -2

Left end point = Phase shift = right p /8

Right end point = Left end point + one period = p /8 + p /2 = p /8 + 4p /8 = 5p /8

Five key points:( p /8, 1), ( p /4, -2), ( 3p /8, -5), ( p /2, -2), ( 5p /8, 1). The first key point occurs at a maximum for the cosine function, we start at the left end point and proceed to the right end point moving in quarter-period increments. The second key point for the cosine function is an average value of the function. The third key point for the cosine function is a minimum. The fourth key point is another average value. The right end point is a maximum value.

Essential Trigonometry, Math Links

by Jack Tompkins