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 for the independent variable, typically denoted as $x$. For example, in the function $y = x + 4$, the domain includes all $x$ values that satisfy the function. To determine the domain, especially for functions involving square roots, set the expression inside the radical to be greater than or equal to zero. For instance, $x + 4 \geq 0$ leads to the domain $x \geq -4$.

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, identify all values that $y$ could take. For $y = x + 4$, the minimum value of $y$ is 0 (when $x = -4$), and the maximum is $\infty$ (when $x = \infty$). Thus, the range is $y \geq 0$.

Exam Tips

• Understand the Definitions: Clearly distinguish between domain and range. Remember, the domain is about possible $x$ values, while the range is about possible $y$ values.
• Use Inequalities: For functions involving square roots or fractions, use inequalities to determine the domain.
• Graphical Insight: Visualize the function graphically to better understand the range and domain.
• Practice with Examples: Solve various examples, like $y = 5x - 2$, to get comfortable with identifying domains and ranges.
• Check Your Work: Always verify your domain and range by substituting values back into the function to ensure they satisfy the equation.