6. (a) Sketch the graph of \(y = \left( \frac { 1 } { 2 } \right) ^ { x } , x \in \mathbb { R }\), showing the coordinates of the point at which the graph crosses the \(y\)-axis.
The table below gives corresponding values of \(x\) and \(y\), for \(y = \left( \frac { 1 } { 2 } \right) ^ { x }\) The values of \(y\) are rounded to 3 decimal places.
| \(x\) | - 0.9 | - 0.8 | - 0.7 | - 0.6 | - 0.5 |
| \(y\) | 1.866 | 1.741 | 1.625 | 1.516 | 1.414 |
(b) Use the trapezium rule with all the values of \(y\) from the table to find an approximate value for
$$\int _ { - 0.9 } ^ { - 0.5 } \left( \frac { 1 } { 2 } \right) ^ { x } d x$$
II