Module 1 Transformations
Benchmark solutions
Stretches:1. a) a = 1/2, b = 3
b) a = 3, b = 1/2
c) a = 4, b = 2
d) a = 1/2, b = 1/4
Combinations:
1. a) reflection in the y axis, translation right 2 units
b) horizontal compression by a factor of 1/2, translation left 4 units and downward 4 units
c) reflection in the y axis, translation right 4 units and upward 5 units
d) horizontal compression by a factor of 1/3, translation right 2 units and upward 8 units
2. a) vertical expansion by a factor of 5, reflection in the x axis, translation right 4 units and upward 80 units.
b) The vertex (0,0) of y = x2 is moved to (4, - 80). the maximum height is 80 m, after 4 seconds.
3. The graph of y = 4cos(2(x - 3)) + 1 is the image of y = cos x after a vertical stretch by a factor of 4, a horizontal stretch by a factor of 1/2, and translation of 3 units right and 1 unit up.