Subjects algebra

Range Definition

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1. The **range** of a function is the set of all possible output values (or $y$-values) that the function can produce. 2. To find the range on a graph, you look at the vertical spread of the graph — that is, all the $y$-values that the graph covers. 3. Specifically, you identify the lowest and highest points on the graph (if they exist) to determine the minimum and maximum values of the range. 4. These points are often called the **minimum** and **maximum** or **extrema** of the function. 5. If the graph extends infinitely up or down, the range will be unbounded in that direction. 6. So, to find the range, look for the $y$-coordinates of the lowest and highest points on the graph, including any horizontal asymptotes or limits if the graph extends infinitely. 7. In summary, the range is all $y$-values between the minimum and maximum points on the graph, including those points if the graph reaches them.