Chapter 4.5, Problem 25E

To determine

To find the relationship between graph of f and g. Consider amplitudes, periods and shifts.

Answer to Problem 25E

The functions f(x) and g(x) have same amplitude.

The functions f(x) and g(x) are similar in phase shift π.

The graph of g(x) is graph of f(x) vertically shift 3 units upwards .

Explanation of Solution

• Compare f(x) with y = d + a cos (bx + c)

Amplitude a = |1| = 1.

Period of a function is 2π/b.

2π/b = 2π/2 =π

Phase Shift of function is -c/b.

-c/b = -0/1 = 0

• Compare g(x) with y = d + a cos (bx + c)

Amplitude a = |1| = 1.

Period of a function is 2π/b.

2π/b = 2π/2 =π

Phase Shift of function is -c/b.

-c/b = -0/1 = 0

• f(x) = cos 2x

  

• g(x) = 3 + cos 2x