Let $f(t)$ be the piecewise linear function with domain $0 \leq t \leq 8$ shown in the graph below (which is determined by connecting the dots). Define a function $A(x)$ with domain $0 \leq x \leq 8$ by

Notice that $A(x)$ is the net area under the function $f(t)$ for $0 \leq t \leq x$. If you click on the graph below, a full-size picture of the graph will open in another window.

 Graph of $y = f(t)$

(A) Find the following values of the function $A(x)$.
$A(0) =$
$A(1) =$
$A(2) =$
$A(3) =$
$A(4) =$
$A(5) =$
$A(6) =$
$A(7) =$
$A(8) =$

(B) Use interval notation to indicate the interval or union of intervals where $A(x)$ is increasing and decreasing.
$A(x)$ is increasing for $x$ in the interval
$A(x)$ is decreasing for $x$ in the interval

(C) Find where $A(x)$ has its maximum and minimum values.
$A(x)$ has its maximum value when $x =$
$A(x)$ has its minimum value when $x =$