Functions

Summary and Exam Tips for Functions

Functions is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. Functions are a fundamental concept in algebra, often represented using function notation such as $f(x)$, which is read as "f of x" and not as a multiplication of $f$ and $x$. This notation is a way to express the y-value in a function, and the y-axis can be labeled as the $f(x)$ axis when graphing. Ordered pairs are written as $(x, f(x))$ instead of $(x, y)$.

To evaluate functions, substitute the given value of $x$ into the function. 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 $f(g(x))$, which is read as "f of g of x". Reciprocal functions, like $f(x) = \frac{1}{x}$, have asymptotes that the graph approaches but never touches. The domain of a reciprocal function excludes values that make the denominator zero, while the range is determined by the inverse function.

Exam Tips

• Understand Function Notation: Ensure you can distinguish between $f(x)$ as a function notation and not a multiplication. This is crucial for interpreting problems correctly.
• Practice Evaluating Functions: Substitute values into functions accurately. Pay attention to parentheses to avoid mistakes in calculations.
• Master Composite Functions: Practice forming and evaluating composite functions like $f(g(x))$ and $g(f(x))$. Understand the order of substitution.
• Reciprocal Functions: Know how to find the domain and range of reciprocal functions. Remember that vertical asymptotes occur where the denominator is zero.
• Graphing Skills: Be comfortable with graphing functions and identifying asymptotes. This will help in visualizing and solving problems effectively.