Domain and Range in MYP Extended Maths

Moving Beyond the Basics

At Standard level, domain and range are introduced intuitively. At Extended level, you are expected to work with formal notation, determine domain and range from equations (not just graphs), and understand why restricting a domain is sometimes mathematically necessary. This topic underpins rational functions, transformations, and any higher-level function work.

Formal Notation

Domain and range are typically expressed using:

• Set notation: {x : x > 0} — read as "the set of x such that x is greater than 0".
• Interval notation: (0, ∞) — open bracket means the endpoint is excluded, square bracket means included. For example, [−3, 5) means −3 ≤ x < 5.
• Inequality notation: x ≥ −3, x < 5 — clear and often used in MYP assessments.

Know all three forms and be able to convert between them.

Determining Domain from an Equation

Ask: what values of x would make this function undefined or impossible?

• Rational functions: exclude x-values that make the denominator zero.
• Square root functions: exclude x-values that make the expression under the root negative.
• Logarithmic functions (if encountered): the argument must be positive.

For polynomial functions (linear, quadratic), the domain is all real numbers unless explicitly restricted.

Determining Range from an Equation or Graph

Range requires understanding what output values the function can produce. For a quadratic f(x) = a(x − h)² + k with a > 0, the minimum output is k, so the range is [k, ∞). For f(x) = 1/x, the output can never equal zero, so the range excludes 0.

Restricting Domains

Sometimes a domain is deliberately restricted — for example, in a real-world model where x represents time and must be non-negative, or to make a function invertible (a one-to-one mapping). At Extended level you should be able to state a restricted domain and explain why it is applied.

Common Mistakes

• Stating the domain of a rational function without checking which x-value makes the denominator zero.
• Confusing open and closed interval brackets — (3, 7] does not include 3 but does include 7.
• Giving the domain as the x-intercepts rather than the full set of valid input values.

Linking to Other Topics

Mastering domain and range pays dividends across all Extended topics: it is needed for rational functions (asymptotes define restrictions), transformations (how transformations affect domain and range), and linear programming (constraints define a feasible domain).