Table of Contents

1. Introduction
2. Basic Concepts
   1. What is a Function?
   2. Why Graph Functions?
3. Graphing Functions using R
   1. Example: Graphing a Linear Function
   2. Example: Graphing a Quadratic Function
4. Conclusion

Introduction

Graphing functions is a fundamental skill in algebra that helps in visualizing the relationship between variables. This document will guide you through the basics of graphing functions, with examples in R programming language.

Basic Concepts

What is a Function?

A function is a relationship between two variables, typically x (independent variable) and y (dependent variable), where each x value is associated with exactly one y value. LaTeX: \( y = f(x) \)

Why Graph Functions?

• To understand the behavior of the function.
• To find key features like intercepts, maxima, minima, and asymptotes.
• To solve equations graphically.

Graphing Functions using R

Example: Graphing a Linear Function

Let's graph the linear function \( y = 2x + 3 \).

library(ggplot2)
x <- seq(-10, 10, by = 0.1)
y <- 2 * x + 3
ggplot(data.frame(x, y), aes(x, y)) +
  geom_line() +
  ggtitle("Graph of y = 2x + 3") +
  xlab("x") + ylab("y")

Example: Graphing a Quadratic Function

Now, let's graph a quadratic function \( y = x^2 - 4x + 4 \).

library(ggplot2)
x <- seq(-10, 10, by = 0.1)
y <- x^2 - 4 * x + 4
ggplot(data.frame(x, y), aes(x, y)) +
  geom_line() +
  ggtitle("Graph of y = x^2 - 4x + 4") +
  xlab("x") + ylab("y")

Conclusion

Graphing functions is a crucial skill in algebra, providing a visual understanding of mathematical relationships. Through practice and the use of tools like R, you can gain deeper insights into the behavior of various functions.