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Comparing Functions

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Comparing Functions

Study Guide

Key Definition

A function is a relation that uniquely associates members of one set with members of another set.

Important Notes

Functions can be represented in various forms: equation, table or graph.
The growth of a function can be linear or non-linear.
For a given input, a function has only one output.

Mathematical Notation

$x$: represents the input of a function

$y$: represents the output of a function

$y = x^2$: represents a quadratic function

$y = x$: represents a linear function

Remember to use proper notation when solving problems

Why It Works

Different functions grow at different rates. A function represented by $y = x^2$ grows faster than a function represented by $y = x$ for sufficiently large positive $x$.

Remember

To compare functions, check their growth rates and values for specific inputs.

Quick Reference

Linear Function:$y = x$

Quadratic Function:$y = x^2$

Understanding Comparing Functions

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In simple terms, comparing functions is about figuring out which function grows faster or is greater for a specific value.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which function grows faster for large positive values of $x$? $y = x$ or $y = x^2$?

Real-World Problem

Question Exercise

Intermediate

Savings Account Scenario

Let's say you have two savings accounts. Account A starts with $100 and increases by $5 each month (linear growth). Account B starts with $100 and doubles each month (exponential growth). Which account grows faster over time?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can a linear function ever grow faster than a quadratic function?

Quick Quiz

Single Choice Quiz

Beginner

For the functions $f(x) = 2x$ and $g(x) = x^2$, which function is greater when $x = 3$?

Recap

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Review key concepts and takeaways