Domain & Range

Domain and Range

Example 1

Find the domain and range of the function f(x) = 2x2? 4x + 1.

Step 1. Determine the domain.

Since this function is not modeling a situation, there is no restriction on the inputs. The domain is FindRangeEx1-1 in other words, the domain is all real numbers.

Step 2. Find the vertex.

FindRangeEx1-2

Step 3. Determine the range.

Since the graph opens up and the vertex is (-1, 3), the range is FindRangeEx1-3 or the set of all y-values that are greater than or equal to 3.