Domain & 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
in other words, the domain is all real numbers.
Step 2. Find the vertex.
Step 3. Determine the range.
Since the graph opens up and the vertex is (-1, 3), the range is
or the set of all y-values that are greater than or equal to 3.