a. Use a graphing utility to graph f(x) = x² + 1.

b. Graph f(x) = x² + 1, g(x) = f(2x), h(x) = f(3x), and k(x) = f(4x) in the same viewing rectangle.

c. Describe the relationship among the graphs of f, g, h, and k, with emphasis on different values of x for points on all four graphs that give the same y-coordinate.

d. Generalize by describing the relationship between the graph of f and the graph of g, where g(x) = f(cx) for c > 1.

e. Try out your generalization by sketching the graphs of f(cx) for c = 1, c = 2, c = 3, and c = 4 for a function of your choice.