Which term describes the set of all possible y-values of a function?

• A. discriminant
• B. range
• C. circumference
• D. width

Answer: (B)

The main idea here is the range of a function—the set of all possible y-values the function can produce. For a function y = f(x), y can take any value that corresponds to some x in the domain, and the collection of those y-values is called the range. For example, with f(x) = x^2, every output is nonnegative, so the range is all y with y ≥ 0. With a straight line y = 2x + 3, you can obtain any real number as an output by choosing an appropriate x, so the range is all real numbers. This differs from terms like discriminant, which relates to the number and nature of roots of a quadratic equation; circumference, which is the distance around a circle; and width, which is a geometric dimension, not the set of outputs of a function. To find the range from a graph, look at the vertical extent—the smallest and largest y-values that occur (or whether the graph goes to infinity in either direction). If there are restrictions, such as square roots requiring nonnegative radicands, those can limit the range accordingly.