Graphs and Functions

Imagine visiting a faraway city or even outer space from the comfort of your living room. It could be possible using virtual reality. This technology creates realistic images that make you feel as if you are truly immersed in the scene and even enable you to interact with them. It is being developed for fun applications, such as video games, but also for architects to plan buildings, car companies to design prototypes, the military to train, and medical students to learn.

Developing virtual reality devices requires modeling the environment using graphs and mathematical relationships. In this chapter, you will graph different relationships and learn ways to describe and analyze graphs.

Sections

• Graph Linear Equations in Two Variables — plotting points, graphing linear equations, graphing vertical and horizontal lines, and finding and using intercepts.
• Slope of a Line — finding and using slope, graphing lines from a point or an intercept, interpreting applications, and identifying parallel and perpendicular lines.
• Find the Equation of a Line — finding equations of lines from a slope and intercept, a slope and point, or two points, including parallel and perpendicular lines.
• Graph Linear Inequalities in Two Variables — verifying solutions, relating solutions to their graphs, graphing linear inequalities, and using them in applications.
• Relations and Functions — finding the domain and range of a relation, determining whether a relation is a function, and evaluating functions.
• Graphs of Functions — using the vertical line test, identifying graphs of basic functions, and reading domain, range, intercepts, and function values from graphs.

This chapter overview is adapted from Intermediate Algebra 2e, Chapter 3 Introduction by Lynn Marecek and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: recast the chapter outline as a descriptive section list.