- (a) Sketch the graph of \(y = 3 ^ { x - 2 } , x \in \mathbb { R }\)
Give the exact values for the coordinates of the point where your graph crosses the \(y\)-axis.
The table below gives corresponding values of \(x\) and \(y\), for \(y = 3 ^ { x - 2 }\)
The values of \(y\) are rounded to 3 decimal places where necessary.
| \(x\) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| \(y\) | 0.192 | 0.333 | 0.577 | 1 | 1.732 | 3 |
(b) Use the trapezium rule with all the values of \(y\) from the table to find an approximate value for
$$\int _ { 0.5 } ^ { 3 } 3 ^ { x - 2 } \mathrm {~d} x$$
Give your answer to 2 decimal places.