About This Chapter
Graphing & Solving Functions - Chapter Summary
In this chapter, our instructors explain how to solve and graph functions. These fun lessons cover transformations, shifting graphs on a plane, graphing reflecting functions and writing exponential functions. You'll also learn about graphing the square root of functions and finding derivatives of implicit functions. By the end of the chapter, you should also be able to:
- Use multiplication and division of ordinates to graph
- Solve problems involving graphing inequalities
- Find the best method for graphing a function
- Use graphs to solve complex real-world problems
- Solve quadratic equations with square roots
You can study at any time you'd like on your mobile device or computer using these professionally-designed learning tools. Each lesson is accompanied by a short quiz that tests your understanding of what you've just learned. Take these lesson quizzes and the chapter test as way to see how you'd do on an upcoming exam. If you need help at any time, feel free to contact one of our instructors for assistance.
1. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
2. Graphing Reflecting Functions
Graphing reflecting functions can come in quite handy in various situations. This lesson will explain relationships between certain functions and their graphs, and we will look at how to graph reflecting functions given one of the functions.
3. Writing & Graphing Exponential Functions
In this lesson, we will explore exponential functions and their properties. Through real world examples and explanation, we will see how to write and graph these types of functions.
4. Graphing Square Roots of Functions
In this lesson you will learn about the characteristics of a square root function and how to graph it. You will also examine in detail the effect the square root sign has on the independent and dependent quantities.
5. How to Find Derivatives of Implicit Functions
How do you define the rate of change when your function has variables that cannot be separated? Learn how implicit differentiation can be used to find dy/dx even when you don't have y=f(x)!
6. Determining the Best Method for Graphing a Function
There are many ways to graph functions. This lesson will go over some common ways to go about this task and discuss how to determine which method is best for a given function.
7. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
8. Solving Quadratic Equations with Square Roots or Graphing the Function
Quadratic equations can be solved in many ways, including taking square roots and graphing the function. In this lesson, learn how to use these techniques to solve quadratic equations.
9. Using Graphs to Solve Complex Problems
Graphing in mathematics is a way of visually representing functions in space. Just as an equation can represent and be used to solve real world problems, so may a function's respective graphical representation.
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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
- Geometrical Representations of Functions
- 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
- 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