Section 4.4: Domain & Range
The domain of a function is the set of all possible inputs (x-values), and the range is the set of all possible outputs (f(x)-values).
Example 1
Find the domain and range of \( f(x) = 2x + 3 \).
Domain: all real numbers \( (-\infty, \infty) \)
Range: all real numbers \( (-\infty, \infty) \)
Example 2
Find the domain and range of \( g(x) = \sqrt{x-1} \).
Domain: \( x \ge 1 \)
Range: \( g(x) \ge 0 \)
Practice Problems
- Find the domain and range of \( h(x) = x^2 \).
- Find the domain and range of \( k(x) = 3 - x \).
- Find the domain and range of \( m(x) = \frac{1}{x} \).
- Find the domain and range of \( p(x) = \sqrt{2x + 4} \).
- Given a table of values, identify the domain and range.