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Functions

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Functions

Study Guide

Key Definition

A function accepts an input, performs a mathematical operation, and returns an output. Each input and output form an ordered pair: $(x, y)$.

Important Notes

Functions represent relationships between two sets of numbers.
Each input $x$ has exactly one output $y$.
They are often written in function notation: $f(x)$.
Functions can be linear, quadratic, and more.
Understanding functions is crucial for advanced math topics.

Mathematical Notation

$\frac{a}{b}$ means fraction

$+$ represents addition

$x^2$ means x squared

$\sqrt{x}$ means square root of x

$\sin(x)$ is the sine function

Remember to use proper notation when solving problems

Why It Works

Functions model real-world situations by linking input values to output results, allowing for predictions and analyses using $formulas$.

Remember

A function's rule often appears as $y = f(x)$, where each input $x$ yields a unique output $y$.

Quick Reference

Linear Function:$f(x) = mx + b$

Quadratic Function:$f(x) = ax^2 + bx + c$

Understanding Functions

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A function maps each input $x$ to an output $y$ using a rule or formula.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the value of $f(x) = 2x + 3$ when $x = 2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A teenager earns $10$ dollars per hour. If they work $h$ hours, express their earnings as a function of $h$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a function $g(x) = x^2 - 4x + 4$ equals zero, find the value of $x$.

Challenge Quiz

Single Choice Quiz

Advanced

For the function $h(x) = \sqrt{x^2 - 4}$, what is the domain of $h(x)$?

Recap

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Review key concepts and takeaways