0580 P42 - Jun 2016 - Q4 - 17 marks
14934
\(f(x)=x^2-\frac1x-4,\quad x\ne0\).
| \(x\) | -3 | -2 | -1 | -0.5 | -0.1 | 0.2 | 0.5 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| \(f(x)\) | 5.3 | 0.5 | -1.8 | 6.0 | -9.0 | -5.8 | -4 | 4.7 |
(a(i)) Complete the table. [2]
(a(ii)) Draw \(y=f(x)\) for \(-3\le x\le-0.1\) and \(0.2\le x\le3\). [5]
(b) Use the graph to solve \(f(x)=0\). [3]
(c) Give an integer \(k\) for which \(f(x)=k\) has one solution. [1]
(d(i)) Draw a suitable straight line to solve \(f(x)+2=-5x\). [4]
(d(ii)) The equation can be written \(x^3+ax^2+bx-1=0\). Find \(a\) and \(b\). [2]
