Composite transformations Problem set B Answers

1. (a) \(y=14 x^{5}\)
2. (b) \(y=5 x^{3} - 2 x^{2}\)
3. (c) \(y=6\times 2^{x+3}\)
4. (d) \(y=3 x^{2} - 3 x - 6\)

1. (a) \(y=25x^2\)
2. (b) 0.2
3. (c) 0.25

1. (a) Turning points: maximum (1, 6) and minimum (3, −10).
2. (b) Turning points: maximum (−4, 1.5) and minimum (−2, −2.5).

1. (a) Turning points: minimum (−1, 1) and maximum (1, 9).
2. (b) Turning points: minimum (−1, −7) and maximum (1, 17).

1. (a) Turning points: maximum (−16, 3) and minimum (−8, −5).
2. (b) Turning points: maximum (1.5, 3) and minimum (2.5, −5).

1. (a) Vertices at (−7, −2), (−4, 10), (−1, 10), (2, −8), (5, −2).
2. (b) Vertices at (−4, 0), (−3, 4), (−2, 4), (−1, −2), (0, 0).

1. (a) Vertical stretch with scale factor 4, then vertical translation by −5.
2. (b) Translation by the vector \(\begin{pmatrix}-2\\-3\end{pmatrix}\) (−2 in the x direction, −3 in the y direction).

1. (a) \(y=0.5^x-5\); \(y=-5\)
2. (b) \(y=-0.5^x+2\); \(y=2\)
3. (c) \(y=5\times0.5^{x-3}+1\); \(y=1\)

\(y=\dfrac{1}{x-4}+1\); asymptotes \(x=4\) and \(y=1\)

1. (a) \(\frac{1}{4}(x-4)^2+2\)
2. (b) Vertical stretch with scale factor 0.25, then translation by the vector \(\begin{pmatrix}4\\2\end{pmatrix}\).

1. (a) Vertical stretch with scale factor 1.5, then translation up 12.
2. (b) Translate up 8, then stretch vertically with scale factor 1.5.

1. (a) Translate 2 left, then stretch horizontally with scale factor 0.25.
2. (b) Stretch horizontally with scale factor 0.25, then translate 2 left.
3. (c) First graph: (−0.5, 0). Second graph: (−2, 0).

(1) Translate by 10 in the x direction, then stretch horizontally with scale factor 0.25. (2) Stretch horizontally with scale factor 0.25, then translate by 2.5 in the x direction.

a = 1, b = 5, c = 3

1. (a) \(y=4f(x)+9\)
2. (b) (2, 29)