Domain and Range

Summary and Exam Tips for Domain and Range

Domain and Range is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. The domain of a function refers to the complete set of possible values of the independent variable, typically denoted as $x$. For example, in the function $y = x + 4$, the domain is determined by the values $x$ can take to satisfy the function. When dealing with square roots, $x$ must be such that the expression inside the root is greater than or equal to zero. For instance, setting $x + 4 \geq 0$ results in a domain of $x \geq -4$.

The range of a function is the complete set of all possible resulting values of the dependent variable, usually $y$, after substituting the domain. To find the range, one must determine all possible values $y$ can take. For the function $y = x + 4$, $y$ has a minimum value of 0 (when $x = -4$) and can increase indefinitely as $x$ increases, leading to a range of $y \geq 0$.

Exam Tips

• Understand the Definitions: Clearly differentiate between the domain (possible $x$ values) and range (possible $y$ values) of a function.
• Solve Step-by-Step: For functions involving square roots, ensure the expression inside the root is non-negative to find the domain.
• Identify Extremes: When determining the range, identify the minimum and maximum values $y$ can take based on the domain.
• Practice with Examples: Work through examples like $y = 5x - 2$ to solidify your understanding of mapping domains to ranges.
• Check Your Work: Always verify your domain and range by substituting back into the original function to ensure consistency.