Stretches and reflections Problem set B Answers

1. (a) maximum (1, 36); x-intercepts −1 and 3; y-intercept (0, 27)
2. (b) maximum (1, 3); x-intercepts −1 and 3; y-intercept (0, 2.25)

1. (a) minimum (1, −4); x-intercepts 1/3 and 5/3; y-intercept (0, 5)
2. (b) minimum (6, −4); x-intercepts 2 and 10; y-intercept (0, 5)

1. (a) Vertical stretch, scale factor 2.5
2. (b) Vertical stretch, scale factor 0.5
3. (c) Horizontal stretch, scale factor 1/3

1. (a) 21x²−42x
2. (b) Vertical stretch, scale factor 3

1. (a) (−4, −3)
2. (b) (5, 8)

1. (a) (8, 2)
2. (b) (−7, −3)

1. (a) vertical stretch, scale factor 4; reflection in the x-axis
2. (b) vertical stretch, scale factor 3; horizontal stretch, scale factor 0.25
3. (c) vertical stretch, scale factor 1/3; reflection in the x-axis
4. (d) vertical stretch, scale factor 2; reflection in the x-axis; horizontal stretch, scale factor 1/3; reflection in the y-axis

1. (a) Greatest depth 4 m; it meets the surface at x = 0 and x = 10 (width unchanged)
2. (b) Greatest depth 2.5 m; width 20 m (from x = 0 to x = 20)
3. (c) y = f(3x), q = 3

1. (a) (5, −3)
2. (b) (−5, 3)

horizontal stretch, scale factor 0.5; reflection in the y-axis

p = 3, q = −2: vertical stretch, scale factor 3; horizontal stretch, scale factor 0.5; reflection in the y-axis