About This Chapter
Graphs & Relations - Chapter Summary
This short but detailed chapter provides instructions on how to create and use graphs for data analysis and problem-solving purposes. You'll develop a better understanding of why graphs are used and how to apply them to real life situations. Each lesson contains examples and illustrations to enhance your review of this material and improve your understanding of these topics. Once you have gone over each of the lessons found in this chapter, you should be able to:
- Interpret straight-line and line segment graphs
- Define step functions and understand how to graph them
- Solve systems of equations
- Find the breakeven point using systems of linear equations
- Apply non-linear functions in the real world
- Describe the use of non-linear graphs and understand interpolation and extrapolation
- Identify the constant of proportionality and use graphing to determine it
Experienced math instructors deliver this material in a simple and engaging manner to make it easily accessible for learners of all levels. You can watch or read lessons at any time, on any device, and even print out transcripts to create handy reference tools. Measure how much you have retained by taking self-assessment quizzes at the end of each lesson.
1. Creating & Interpreting Straight-Line & Line Segment Graphs
Straight-line graphs and line segment graphs are very useful in many different fields. In this lesson, we will explore how to create line graphs and how to interpret the meaning of these graphs.
2. How to Graph Step Functions
In this lesson, we'll learn the definition of a step function and two of its family members: floor functions and ceiling functions. We'll then look at how to graph step functions using two real world examples.
3. Solving a System of Equations with Two Unknowns
When you have two variables and two equations, is solving the problem four times as hard? No! Not when you use the substitution or elimination method to solve systems of equations. We'll practice both in this lesson.
4. Applying Systems of Linear Equations to Breakeven Point: Steps & Example
Businesses use breakeven points to determine price and sell products. Learn how to use systems of linear equations with revenue and cost functions to find the breakeven point.
5. Using Nonlinear Functions in Real Life Situations
In this lesson, we will define non-linear functions and look at examples of non-linear functions being used in real-world situations. We will also touch on determining which non-linear function is best to use in different real-world scenarios.
6. Modeling With Nonlinear Graphs
Graphical depictions of functions serve as a means of conceptualizing (aiding in understanding) a plethora of mental constructs in physical science. Non-linear functions are used to represent a variety of phenomena, like those relating to motion for instance. A straight-forward example of such a non-linear function and its graph will be presented.
7. Identifying the Constant of Proportionality
Constants of proportionality might sound like something complicated, but chances are, you've encountered them before. In this lesson, we'll explore the constant of proportionality and how to find it.
8. Using Graphs to Determine the Constant of Proportionality
Because the constant of proportionality only exists for linear relationships, you can use the graph of a proportional relationship to figure out what your constant of proportionality is. Learn how in this lesson.
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Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
- Population & Samples
- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
- Correlation & Causation in Math
- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Paths & Circuits
- Problem Solving With Networks
- Geometric Solids
- Measurement & Trigonometry
- Spherical Geometry
- Applications of Spherical Geometry
- Linear Programming Overview
- VCE Further Mathematics Flashcards