Nonlinear Functions

Question

Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to −4?

A. y=x²−6

B. y=x³−6

C. y=|x|−6

D. y=(x−6)²

Answer 1

The easiest thing to do is to graph each of the functions (on a calculator, online, or manually), add a horizontal line for the function y = -4, then see which graph lies completely above the horizontal line (never intersects it).

Note, in this specific question, plugging in x = 0 gives y = -6 for all of the functions except the last one, so that must be the answer!