### Home > APCALC > Chapter 1 > Lesson 1.3.3 > Problem 1-131

1-131.

Examine two ways a line changes: Homework Help ✎

Sketch

*f*(*x*) = 4*x*+ 1. What are*f*(0),*f*(1),*f*(2), and*f*(3)? How are the function values changing as*x*increases?Compute the finite differences (that is, find the difference in

*y*-values as*x*increases) and look for a pattern.Calculate the area under the curve for 0 ≤

*x*≤*a*if*a*= 0, 1, 2, and 3. How is the area changing as*a*increases?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?