Domain and range

The allowed x-values and the resulting y-values of a function. CAPS Grade 12 definition, worked NSC example and related functions practice.

The allowed x-values and the resulting y-values of a function.

Definition

The domain is the set of all input (x) values for which a function is defined. The range is the set of all output (y) values the function can produce.

Worked example

For y = √(x − 2), the domain is x ≥ 2 and the range is y ≥ 0.

Where it appears in the exam

Short Paper 1 questions ask for the domain or range of a hyperbola, parabola or exponential function in inequality or interval notation.

Step-by-step method

  1. Find any x-values that are not allowed (division by zero, a negative under a square root, a restricted domain).
  2. Write the domain as x ∈ ℝ with those exclusions.
  3. Use the turning point or asymptote to find the smallest or largest y-value.
  4. Write the range in inequality or interval notation.

Common mistake

Giving a parabola's range from the x-coordinate of the turning point instead of the y-coordinate.

Related functions terms

Frequently asked questions

What does domain and range mean in Grade 12 Maths?

The domain is the set of all input (x) values for which a function is defined. The range is the set of all output (y) values the function can produce.

Which NSC paper tests domain and range?

Domain and range belongs to the Functions section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving domain and range?

Snap a question that uses domain and range into the Snap&Learn AI solver, or work through the functions topic guide and NSC past papers.

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