Examine two ways a line changes:

1. Sketch $f(x) = 4x + 1$. Find $f(0)$, $f(1)$, $f(2)$, and $f(3)$. How are the function values changing as $x$ increases?

   Hint (a):

   Compute the finite differences (that is, find the difference in $y$-values as $x$ increases) and look for a pattern.
   

2. Find $A(f, 0 ≤ x ≤ a)$ for $a = 0, 1,2,$ and $3$. How are the areas changing as $a$ increases?

   Hint (b):

   Use geometry to find the area of the trapezoid between $x = 0$ and $x = 2$ for each value of $a$. Keep your results organized.

   More Help (b):

   Is the difference between the areas growing constantly or linearly? If not, how else could it be growing, and by what pattern each time?