Range

Definition

The range of a function is the set of all possible output values (y-values) that the function can produce. It is determined by evaluating the function over its domain.

5 Must Know Facts For Your Next Test

1. The range depends on the behavior and type of the function, such as linear, quadratic, or exponential.
2. To find the range, analyze the function's formula and consider any restrictions or asymptotes.
3. Graphing a function can help visually determine its range by observing the vertical extent of the graph.
4. $f(x) = \sqrt{x}$ has a range of $[0, \infty)$ because square roots cannot produce negative numbers.
5. $f(x) = \frac{1}{x}$ has a range of $(-\infty, 0) \cup (0, \infty)$ because it never reaches zero.

Review Questions

• What is the range of $f(x) = x^2$?
• How would you determine the range of an exponential function like $f(x) = e^x$?
• Why can't $f(x) = \frac{1}{x}$ have zero in its range?

Related terms

Domain:

The set of all possible input values (x-values) for which a function is defined.

Function:

A relation between a set of inputs and a set of permissible outputs with each input related to exactly one output.

Asymptote: A line that a graph approaches but never touches or crosses.