CPM Homework Help : PC Problem 8-11

Given the piecewise function $h ( t ) = \left\{ \begin{array} { l l l } { 4 } & { \text { for } } & { 0 \leq t \leq 4 } \\ { t } & { \text { for } } & { 4 < t < 6 } \\ { 6 } & { \text { for } 6 \leq t \leq 10 } \end{array} \right.$ , complete the following problems.

Graph $h\left(t\right)$ over the interval $0 ≤ t ≤ 10$ .
Answer (a):
What is the area under $h\left(t\right)$ over the interval $≤ t ≤ 10$ ?
Hint (b):
Break the area into smaller rectangles and triangles. Calculate the area for each. Add up the areas of the parts.
If $g\left(t\right) = h\left(t\right) + 6$ , what is the area under $g\left(t\right)$ for the same interval?
Hint (c):
Raising the graph up $6$ would give the area an additional $\left(6\right)\left(\text{width}\right)$ .

Continuous linear piecewise, starting at (0, comma 4), turning at (4, comma 4), (6, comma 6), ending at (10, comma 6).

Added to piecewise, vertical segments from function to x axis, at x = 1, 4, 6, & 10, & horizontal segment between (4, comma 4), ( 6, comma 4), area between function & x axis shaded.