Range

Definition

The range of a function is the set of all possible output values it 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 function's type and its domain.
2. For trigonometric functions like sine and cosine, the range is typically between -1 and 1.
3. Inverse trigonometric functions have specific ranges to ensure they are one-to-one functions.
4. To find the range of a quadratic function, you can use its vertex form.
5. Graph analysis can help determine the range by observing the highest and lowest points on the graph.

Review Questions

• What is the range of $f(x) = \sin(x)$?
• How do you determine the range of an inverse trigonometric function?
• Describe how to find the range of a quadratic function given in standard form.

Related terms

Domain: The set of all possible input values for which a function is defined.

Inverse Function: A function that reverses another function, meaning if $f(x) = y$, then $f^{-1}(y) = x$.

Vertex Form: $$y = a(x-h)^2 + k$$, where $(h, k)$ is the vertex of a quadratic function.