The table below is for y = x³ - 3x - 1 . X -3 -2 -1 0 1 2 3 y -19 -3 1 -1 -3 1 [Figure: Graph grid provided for plotting]

1. (a)Complete the table.[1]
2. (b)On the grid, draw the graph of y = x³ - 3x - 1 .[3]
3. (c)Use your graph to solve x³ - 3x - 1 = 0 .[2]
4. (d)Use your graph to estimate the gradient of the curve when x = -1.5 .[2]
5. (e)(i)On the grid draw the graph of y = 4x + 3.[1]
6. (e)(ii)The line y = 4x +3 and the curve y = x³ - 3x - 1 can be used to solve the equation x³ = ax + b . Find the values of a and b.[2]
7. (e)(iii)Use your graph to find one of the negative solutions of x³ = ax + b .[1]

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