MATH 180 FALL 1995

ASSIGNMENT #6

1.9, #1. Stretching the graph of y = x^{2} vertically by a factor of 2 gives the graph of y = 2x^{2}. Shifting this last graph upwards by one unit gives the graph of y − 1 = 2x^{2} or y = 2x^{2} + 1. Now interchange the order of the stretch and shift operations. Shifting the graph of y = x^{2} upwards gives the graph of y − 1 = x^{2} or y = x^{2} + 1. Stretching this last graph vertically by a factor of 2 gives the graph of y = 2x^{2} + 2. So interchanging the operations gives a different graph. Comment: The incorrect answer y = x^{2} + 2 was given for part (b) by a number of students. Compare this with the answer given above.

1.9, #2. g(f(x)) = log(2x + 3), f(g(x)) = (2 log x) + 3, f(f(x)) = 2(2x + 3) + 3 = 4x + 9.

1.10, #20, 21. The period of the earth’s revolution around the sun is about a year or 365 days. The period of the moon’s revolution around the earth is about 29 days.

1.10, #33, 35. Possible functions are y = 2 sin(x/4) and y = 5 cos(x/3). A common mistake: Writing 4x and 3x instead of x/4 and x/3.