About This Chapter
How It Works:
- Identify the lessons in the OUP Mathematical Models chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the mathematical model topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
You'll learn all of the math topics covered in the textbook chapter, including:
- Key terms related to functions
- Graphing functions
- Domain and range
- Real-life linear models
- Quadratic equations
- Exponential functions
- Exponential growth and decay
- Polynomials in function notation
- Polynomial graphs
- Graph construction
- The interpretation of line graphs
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1. What is a Function: Basics and Key Terms
In calculus, functions map one set of numbers of another set of numbers, such as calculating the price of something bought by the pound. Learn about the basics of a function, examples of functions utilized in everyday life, the definitions of key terms like domain and range, and how to create a function and graph it.
2. Graphing Basic Functions
Graphing basic functions on a Cartesian plane is similar to finding a spot on a map. Learn more about the similarities between maps and graphs, the functions of ordered pairs and quadrants, and how to graph their functions.
3. What Is Domain and Range in a Function?
The domain is the set of all the allowable input values of a function, while the range is the set of all possible output of the function. Learn how to find the domain and range of a function through given values, graphs, or general function rules.
4. Writing & Evaluating Real-Life Linear Models: Process & Examples
Writing and evaluating real-life linear models is the mathematical process of comparing the rate of change between two values. Learn about rate of change as well as the process of writing and evaluating linear equations through real-world examples of linear models.
5. What is a Quadratic Equation? - Definition & Examples
A quadratic equation is a second-degree equation with one unknown variable. Explore the definition and examples of a quadratic function, the graph of a quadratic equation, when a quadratic equation can have two solutions, and why quadratics are important.
6. Parabolas in Standard, Intercept, and Vertex Form
The equation of a parabola can be expressed in three different forms. Explore different kinds of parabolas, and learn about the standard form, the intercept form, and the vertex form of parabola equations.
7. What Is an Exponential Function?
Exponential functions have a constant base with an independent variable that is an exponent, such as y = ab^x. Learn more about functions with exponents and find two examples that demonstrate the way exponential functions appear on graphs.
8. Exponential Growth vs. Decay
Exponential growth and decay are the results of a continuous pattern of numbers found in exponential fractions. Learn more about the differences between exponential growth and exponential decay, and learn how to solve more complex problems by determining a starting value.
9. How to Evaluate a Polynomial in Function Notation
A polynomial is an algebraic expression that has more than one term and function notation is the way a function is written. In this lesson, explore how to evaluate or solve a polynomial in function notation.
10. Understanding Basic Polynomial Graphs
Understanding basic polynomial graphs requires knowing about their degrees and leading coefficients. Learn more about the implications of exponents and leading coefficients in polynomial graphs. Discover also how turning points are determined in graphing polynomials.
11. How to Construct Graphs from Data
Graphs provide a visual representation of numerical and categorical data. Explore the proper way to construct pie graphs and line graphs to display different types of information.
12. Reading and Interpreting Line Graphs
Line graphs, with lines connecting points of data to each other, can provide insights into various kinds of data. Through various examples, learn how to read and interpret different line graphs.
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Other chapters within the OUP Oxford IB Math Studies: Online Textbook Help course
- OUP Oxford IB Math Studies Chapter 1: Number & Algebra 1
- OUP Oxford IB Math Studies Chapter 2: Descriptive Statistics
- OUP Oxford IB Math Studies Chapter 3: Geometry & Trigonometry 1
- OUP Oxford IB Math Studies Chapter 5: Statistical Applications
- OUP Oxford IB Math Studies Chapter 6: Introducing Differential Calculus
- OUP Oxford IB Math Studies Chapter 7: Number & Algebra 2
- OUP Oxford IB Math Studies Chapter 8: Sets & Probability
- OUP Oxford IB Math Studies Chapter 9: Logic
- OUP Oxford IB Math Studies Chapter 10: Geometry & Trigonometry 2
- OUP Oxford IB Math Studies Chapter 13: Prior Learning