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Writing Number Patterns in Function Notation

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Writing Number Patterns in Function Notation

Study Guide

Key Definition

A function is a relation where each input has a single output. For example, $f(x) = x + 8$ can describe an arithmetic sequence.

Important Notes

Arithmetic sequences increase by a constant value: $f(x) = x + d$
Function notation helps in generating terms in a sequence without listing them all.
The constant difference in an arithmetic sequence is crucial in defining the function.
Understanding input-output relationships aids in writing functions.
Patterns can be expressed mathematically to predict future terms.

Mathematical Notation

$f(x)$ represents a function of $x$

$x^2$ denotes $x$ squared

$\frac{a}{b}$ is a fraction with $a$ as numerator and $b$ as denominator

$\sqrt{x}$ represents the square root of $x$

$+$ represents addition

Remember to use proper notation when solving problems

Why It Works

Functions like $f(x) = 2x + 3$ provide a formulaic method to calculate the nth term in a sequence efficiently.

Remember

For an arithmetic sequence with first term $a$ and common difference $d$, the nth term is $a + (n-1)d$

Quick Reference

Arithmetic Sequence Formula:$a_n = a + (n-1)d$

Understanding Writing Number Patterns in Function Notation

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Video explanation of this concept

Beginner

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Beginner Explanation

An arithmetic sequence is a list of numbers where each term increases by a constant amount called the common difference, d. We write functions like $f(x) = x + d$ to represent this, where x is the term number. For example, if d = 3, then f(1) = 1 + 3 = 4 gives the first term, f(2) = 2 + 3 = 5 gives the second term, and so on. This notation helps us quickly find any term in the sequence without listing all previous terms.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the function for the sequence: 3, 7, 11, 15?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You save $5 every week. What function represents your savings after x weeks?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the 100th term of the sequence 2, 10, 18, 26,...

Challenge Quiz

Single Choice Quiz

Advanced

What is the 50th term of the sequence given by $f(x) = 3x - 2$?

Recap

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Review key concepts and takeaways