Functions

Summary and Exam Tips for Functions

Functions is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. In mathematics, functions are a fundamental concept used to describe relationships between variables. The most common notation is $f(x)$, read as "f of x", which represents the y-value in a function. This notation is not a multiplication of $f$ and $x$. Functions are often named with single letters like $f$, $g$, or $h$. Evaluating a function involves substituting a specific value for $x$ in the function expression. For example, if $f(x) = 3x - 5$, then $f(4) = 7$, which can be represented as the ordered pair $(4, 7)$.

Composite functions are formed by substituting one function into another, such as $f(g(x))$, also written as $(f \circ g)(x)$. Reciprocal functions, like $f(x) = \frac{1}{x}$, have asymptotes, which are lines the graph approaches but never touches. The domain of a reciprocal function excludes values that make the denominator zero, and the range excludes values that make the inverse function's denominator zero. For instance, the domain of $y = \frac{1}{x+3}$ is all real numbers except $x = -3$, and the range is all real numbers except 0.

Exam Tips

• Understand Function Notation: Remember that $f(x)$ is not a multiplication. It represents the output of the function for a given input $x$.
• Evaluate Functions Carefully: Substitute values into the function with precision, using parentheses to avoid errors in calculations.
• Composite Functions: Practice forming and evaluating composite functions, such as $f(g(x))$ and $g(f(x))$, to understand how functions interact.
• Reciprocal Functions: Identify vertical and horizontal asymptotes by analyzing the function's form. Remember that the domain excludes values that make the denominator zero.
• Practice Problems: Regularly solve practice questions to reinforce your understanding and improve problem-solving speed.