### Home > CALC > Chapter Ch1 > Lesson 1.3.3 > Problem 1-131

1-131.

Examine two ways a line changes: Homework Help ✎

Sketch

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

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

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

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

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