Stretches and reflections Problem set A Answers

1. (a) maximum (3, 12); x-intercepts 1 and 5; y-intercept (0, −15)
2. (b) maximum (3, 2); x-intercepts 1 and 5; y-intercept (0, −2.5)

1. (a) minimum (0.5, −4); x-intercepts −0.5 and 1.5; y-intercept (0, −3)
2. (b) minimum (3, −4); x-intercepts −3 and 9; y-intercept (0, −3)

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

1. (a) 36x²−24x
2. (b) Vertical stretch, scale factor 4

1. (a) (3, 5)
2. (b) (−6, −2)

1. (a) (−4, −1)
2. (b) (3, −7)

1. (a) vertical stretch, scale factor 2; reflection in the x-axis
2. (b) vertical stretch, scale factor 5; horizontal stretch, scale factor 0.5
3. (c) vertical stretch, scale factor 0.5; reflection in the x-axis
4. (d) vertical stretch, scale factor 3; reflection in the x-axis; horizontal stretch, scale factor 0.5; reflection in the y-axis

1. (a) Greatest height 12 m; it meets the ground at x = 0 and x = 8 (width unchanged)
2. (b) Greatest height 8 m; width 16 m (from x = 0 to x = 16)
3. (c) y = f(2x), q = 2

1. (a) (−6, 4)
2. (b) (6, −4)

reflection in the x-axis; horizontal stretch, scale factor 2

p = −3, q = 3: vertical stretch, scale factor 3; reflection in the x-axis; horizontal stretch, scale factor 1/3