Domain Visualization with Number Lines
Legend:
Included (closed circle)
Excluded (open circle)
Included in domain (blue line)
Example 1: f(x) = 1/(x-3)
Domain: All real numbers except x = 3
Interval notation: (-∞, 3) ∪ (3, ∞)
Example 2: g(x) = √(x-5)
Domain: All real numbers greater than or equal to 5
Interval notation: [5, ∞)
Example 3: h(x) = 1/((x-2)(x+4))
Domain: All real numbers except x = -4 and x = 2
Interval notation: (-∞, -4) ∪ (-4, 2) ∪ (2, ∞)
Example 4: f(x) = 1/√(x-a) where a = 3
Domain: All real numbers greater than 3
Interval notation: (3, ∞)
