f(x) = x³ (a) Complete the following table.

1. (a)Complete the following table. X | -3 | -2 | -1 | 0 | 1 | 2 | 3 f(x)| | | | | | |[1]
2. (b)Using a scale of 2 cm to represent 1 unit, draw a horizontal x-axis for −3 ≤ x ≤ 3. Using a scale of 2 cm to represent 10 units, draw a vertical y-axis for −30 ≤ y ≤ 30. Using your axes, plot the points in the table and join them with a smooth curve.[2]
3. (c)(i)Use your graph to solve f(x) = -15.[1]
4. (c)(ii)Use your graph to find a such that f¯¹ (a) = 1.7 .[1]
5. (c)(iii)Given that f¯¹(t) = u, express t in terms of u.[1]
6. (c)(iv)By drawing a tangent to y = f(x), estimate the gradient of the curve when x = 2.[2]
7. (d)(i)Using the same axes draw the line that represents the function g(x) = 5x + 3 .[2]
8. (d)(ii)Hence find the three solutions of the equation f(x) = g(x) .[2]

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