ISEE Upper Level Mathematics Achievement

ISEE Upper Level Mathematics Achievement focuses on advanced mathematical concepts and problem-solving skills necessary for success in the ISEE exam.

Advanced Topics

Functions and Patterns

Discovering Patterns with Functions

Functions are like machines: you put something in (an input), and the machine gives you something out (an output).

What is a Function?

A function takes an input (often called \( x \)) and produces exactly one output (often called \( y \)). You might see it written as \( y = f(x) \).

Recognizing Patterns

Sequences and patterns can often be described using functions or rules. For example, the sequence 2, 4, 6, 8... follows the rule \( y = 2x \).

Using Functions

Functions can model real-life relationships, like the total cost of movie tickets based on the number bought.

Real-World Connection

Predicting the next term in a pattern or calculating your phone bill are both examples of using functions!

Key Formula

\[y = f(x)\]

Examples

  • If each concert ticket costs $15, the total cost is \( y = 15x \) where x is the number of tickets.

  • The pattern 3, 6, 9, 12... can be described by \( y = 3x \).

In a Nutshell

Functions describe how one quantity depends on another, revealing hidden patterns.

Key Terms

Function
A relationship that assigns exactly one output to each input.
Sequence
An ordered list of numbers following a particular pattern.