Composite transformations Problem set A Answers

1. (a) \(y=30 x^{4}\)
2. (b) \(y=4 x^{3} + x^{2}\)
3. (c) \(y=5\times 3^{x-2}\)
4. (d) \(y=2 x^{2} - 4 x - 6\)

1. (a) \(y=16x^2\)
2. (b) 0.25
3. (c) 0.2

1. (a) Turning points: maximum (0, 6) and minimum (2, −6).
2. (b) Turning points: maximum (5, 1) and minimum (7, −1).

1. (a) Turning points: minimum (1, 0) and maximum (3, 4).
2. (b) Turning points: minimum (1, −3) and maximum (3, 5).

1. (a) Turning points: maximum (4, 2) and minimum (8, −2).
2. (b) Turning points: maximum (2, 2) and minimum (3, −2).

1. (a) Vertices at (−3, 3), (−1, −5), (1, −5), (3, 5), (5, 5).
2. (b) Vertices at (−4, 1), (−3, −3), (−2, −3), (−1, 2), (0, 2).

1. (a) Vertical stretch with scale factor 3, then vertical translation by 4.
2. (b) Translation by the vector \(\begin{pmatrix}4\\1\end{pmatrix}\) (4 in the x direction, 1 in the y direction).

1. (a) \(y=3^x+2\); \(y=2\)
2. (b) \(y=-3^x+5\); \(y=5\)
3. (c) \(y=4\times3^x-1\); \(y=-1\)

\(y=\dfrac{1}{x+3}-2\); asymptotes \(x=-3\) and \(y=-2\)

1. (a) \(\frac{1}{2}(x-6)^2+3\)
2. (b) Vertical stretch with scale factor 0.5, then translation by the vector \(\begin{pmatrix}6\\3\end{pmatrix}\).

1. (a) Vertical stretch with scale factor 1.8, then translation up 32.
2. (b) Translate up 160/9, then stretch vertically with scale factor 1.8.

1. (a) Translate 3 right, then stretch horizontally with scale factor 0.2.
2. (b) Stretch horizontally with scale factor 0.2, then translate 3 right.
3. (c) First graph: (0.6, 0). Second graph: (3, 0).

(1) Translate by −3 in the x direction, then stretch horizontally with scale factor 1/6. (2) Stretch horizontally with scale factor 1/6, then translate by −0.5 in the x direction.

a = 1, b = 4, c = 12

1. (a) \(y=5f(x)+4\)
2. (b) (3, 24)