About This Chapter
Geometrical Representations of Functions - Chapter Summary
This informative chapter covers the geometrical representations of functions. Our lessons explain dependent and independent variables as they're used in math and the notation and identification used in functions, plus practice problems. You'll also learn about domain and range in a function and the basics of graphing that relate to functions. This chapter is designed to help you:
- Evaluate algebraic expressions for 2D geometric figures
- Define locus of points
- Graph a system of inequalities, including the feasible region
- Explain the different types of coordinate systems in geometry
The most challenging topics are made simple with our professionally designed and user-friendly learning tools. Each video or text lesson has been created by an instructor to make your learning experience interesting and fun. If you want to go back and review just one part of a video lesson, use the video tabs feature found in the Timeline. Feel free to reach out to an instructor if you need assistance along the way.
1. Independent & Dependent Variables in Math
Learn what it means for a variable to be independent or dependent. Then explore how we identify which variables are independent and which are dependent in word problems and math equations.
2. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
3. What Is Domain and Range in a Function?
The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.
4. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
5. Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures
Learning more about algebraic expressions and geometric figures will help you solve problems that occur in your life. In this lesson, you will use the perimeter of a two-dimensional geometric shape to solve a real-world problem.
6. Locus of Points: Definition, Methods & Examples
In this lesson, we will define a locus of points. We will look at various examples of a locus of points, and we will look at an example of finding an equation representing a locus of points in a real-world setting.
7. Graphing the Feasible Region of a System of Inequalities
The feasible region of a system of inequalities is the area of the graph containing the points that satisfy all the inequalities at once. Watch this lesson to learn how to graph one.
8. Coordinate System in Geometry: Definition & Types
Coordinate systems use 1-dimensional, 2-dimensional and 3-dimensional spaces and coordinates to define points. The ''xy'' coordinate grid is the most common of these systems, which you can learn how to use in this lesson.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards