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

  1. Find the domain and range of \( h(x) = x^2 \).
  2. Find the domain and range of \( k(x) = 3 - x \).
  3. Find the domain and range of \( m(x) = \frac{1}{x} \).
  4. Find the domain and range of \( p(x) = \sqrt{2x + 4} \).
  5. Given a table of values, identify the domain and range.