Carefully graph the function   $f ( x ) = \left\{ \begin{array} { c c } { 3 x + 4 } & { \text { for } x < 1 } \\ { - \frac { 1 } { 2 } x + 5.5 } & { \text { for } x \geq 1 } \end{array} \right.$          .

1. Iveta wants to calculate the area under the curve for $−1 ≤ x ≤ 5$, so she decides to divide the region into ten trapezoids to approximate the area. Explain to Iveta why this is not the most efficient method.

   Hint (a):

   Can you find a way to calculate the area accurately with less than $10$ trapezoids?

   Answer (a):

   Because the function is composed of two linear pieces, the exact area can be computed using two trapezoids.

2. Calculate the area under the curve for $−1 ≤ x ≤ 5$.