# Ch 12: Michigan Merit Exam - Math: Working with Functions

### About This Chapter

## Michigan Merit Exam - Math: Working with Functions - Chapter Summary

Learn the definition of a piecewise function by watching one of this chapter's video lessons. Quiz yourself to see if you have grasped the concepts of composite functions and inverse functions. The study guides in this chapter will help you become knowledgeable about the following:

- Plane graphs
- Operations and functions
- Decoding piecewise functions
- Ways of creating functions
- Composite functions
- Graphing functions, compound functions, and inverse functions
- Function families
- Function families and real-life situations

Any questions that may arise as you move through the chapter can be answered by our instructors or experts. You can see the parts of the videos that explain the correct answers to your quiz questions by clicking the 'Watch Answer' buttons. Lesson transcripts are also available for your review.

### Michigan Merit Exam - Math: Working with Functions Objectives

This chapter relates to the Algebra and Functions domain of the 4-part math portion of the Michigan Merit Exam. The math portion will contain approximately 25 multiple-choice questions for you to answer. Questions about how to display a function on a graph and define a piecewise function may also appear on the exam.

### 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. How to Add, Subtract, Multiply and Divide Functions

Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!

### 3. Translating Piecewise Functions

Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.

### 4. How to Compose Functions

Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.

### 5. Domain & Range of Composite Functions: Definition & Examples

Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.

### 6. Compounding Functions and Graphing Functions of Functions

We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!

### 7. Inverse Functions

Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.

### 8. Understanding and Graphing the Inverse Function

If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.

### 9. How to Identify Families of Functions

Functions come in all kinds of varieties, but they can be grouped together into families that have common characteristics. The difference and similarities can be seen in the equations and graphs of these functions. In this lesson, you will learn about the characteristics of different families of functions and how to recognize them based on their equations and graphs.

### 10. Modeling the Real World with Families of Functions

Families of functions are exactly as their name indicates, groups of functions that are all related in a specific way. Let's look at families of functions and use examples to see how to use them to model and analyze real-world phenomena.

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### Other Chapters

Other chapters within the Michigan Merit Exam - Math: Test Prep & Practice course

- Michigan Merit Exam - Math: Number Systems & Number Sense
- Michigan Merit Exam - Math: Representations & Relationships
- Michigan Merit Exam - Math: Counting & Probabilistic Reasoning
- Michigan Merit Exam - Math: Using Real & Complex Numbers
- Michigan Merit Exam - Math: Sequences & Iteration
- Michigan Merit Exam - Math: Measurement Units, Calculations & Scales
- Michigan Merit Exam - Math: Understanding Error
- Michigan Merit Exam - Math: Mathematical Reasoning
- Michigan Merit Exam - Math: Language, Laws & Proof of Logic
- Michigan Merit Exam - Math: Using Algebraic Expressions
- Michigan Merit Exam - Math: Properties of Functions
- Michigan Merit Exam - Math: Lines & Linear Functions
- Michigan Merit Exam - Math: Absolute Values
- Michigan Merit Exam - Math: Inequalities
- Michigan Merit Exam - Math: Exponential & Logarithmic Functions
- Michigan Merit Exam - Math: Quadratic Functions
- Michigan Merit Exam - Math: Power Functions
- Michigan Merit Exam - Math: Polynomial Functions
- Michigan Merit Exam - Math: Rational Functions
- Michigan Merit Exam - Math: Trigonometric Functions
- Michigan Merit Exam - Math: Euclidean & Coordinate Geometry
- Michigan Merit Exam - Math: Triangles & Their Properties
- Michigan Merit Exam - Math: Triangles & Trigonometry
- Michigan Merit Exam - Math: Quadrilaterals & Their Properties
- Michigan Merit Exam - Math: Other Polygons & Their Properties
- Michigan Merit Exam - Math: Circles & Their Properties
- Michigan Merit Exam - Math: Conic Sections & Their Properties
- Michigan Merit Exam - Math: 3D Figures
- Michigan Merit Exam - Math: Comparing Area & Volume Formulas
- Michigan Merit Exam - Math: 2D & 3D Representations
- Michigan Merit Exam - Math: Congruence & Similarity
- Michigan Merit Exam - Math: Transformations & Isometries
- Michigan Merit Exam - Math: Dilations & Isometries
- Michigan Merit Exam - Math: Creating & Interpreting Plots
- Michigan Merit Exam - Math: Measures of Center & Variation
- Michigan Merit Exam - Math: The Normal Distribution
- Michigan Merit Exam - Math: Scatterplots & Correlation
- Michigan Merit Exam - Math: Linear Regression
- Michigan Merit Exam - Math: Data Collection & Analysis
- Michigan Merit Exam - Math: Probability
- Michigan Merit Exam - Math: Application & Representation
- Michigan Merit Exam - Math Flashcards