REFLECTIONS OF THE toolkit FUNCTION \(f(x) = b^x\), Example \(\PageIndex{5}\): Writing and Graphing the Reflection of an Exponential Function. For example, if we begin by graphing the toolkit function \(f(x)=2^x\), we can then graph the stretch, using \(a=3\), to get \(g(x)=3(2)^x\) as shown on the left in Figure \(\PageIndex{8}\), and the compression, using \(a=\frac{1}{3}\), to get \(h(x)=\frac{1}{3}{(2)}^x\) as shown on the right in Figure \(\PageIndex{8}\). ��-뚕� ����p6�U� Now, let me show you something very cool about the equations of the graphs of these constant ratio points. If [latex]{a}_{1}[/latex] is the initial term of a geometric sequence and [latex]r compressed vertically by a factor of \(|a|\) if \(0<|a|<1\). For example, think of the model toys that some people build. Plus, get practice tests, quizzes, and personalized coaching to help you Students: Use Video Games to Stay in Shape, Associate of Film and Video: Degree Overview, Video Production Assistant: Employment & Career Info, Biology Lesson Plans: Physiology, Mitosis, Metric System Video Lessons, Free Video Lecture Podcasts From Top Universities, Best Free Online Video Lectures: Study.com's People's Choice Award Winner, Best Non-Video Free Courses: Study.com's People's Choice Award Winner, Production Operator: Job Description, Duties and Requirements, Executive Administrative Assistant: Employment Info & Career Requirements, Behavior Modification Courses and Classes Overview, Overview of Biostatistics Lectures and Courses, Tips for Writing an Effective Cover Letter, Students Go Back to School Student Suspensions Begin, Problems with Radical Expressions & Equations, Problems with Algebraic Expressions and Equations, Algebraic Linear Equations & Inequalities, Calculations with Ratios, Percent & Proportions, Graphing Quantity Values With Constant Ratios, Triangles, the Pythagorean Theorem & Congruency, Statistics, Probability & Working with Data, Introduction to Statistics: Homework Help Resource, TExES Music EC-12 (177): Practice & Study Guide, High School Algebra II: Homework Help Resource, FTCE Business Education 6-12 (051): Test Practice & Study Guide, The Great Global Conversation: Reading Passages on the SAT, Quiz & Worksheet - Government Corporations, Quiz & Worksheet - Research Tools in Developmental Psychology, Quiz & Worksheet - Lines in Musical Notation, Quiz & Worksheet - Nonstandard Musical Notation Symbols, Quiz & Worksheet - Articulation, Dynamic & Expression Symbols, NYSTCE English Language Arts: Writing Style, NYSTCE English Language Arts: Narrative & Descriptive Writing, NYSTCE English Language Arts: Research & Writing Tips, NYSTCE English Language Arts: Interpersonal Communication, NYSTCE English Language Arts: Communicating in Groups, CPA Subtest IV - Regulation (REG): Study Guide & Practice, CPA Subtest III - Financial Accounting & Reporting (FAR): Study Guide & Practice, ANCC Family Nurse Practitioner: Study Guide & Practice, Top 50 K-12 School Districts for Teachers in Georgia, Finding Good Online Homeschool Programs for the 2020-2021 School Year, Coronavirus Safety Tips for Students Headed Back to School, Parent's Guide for Supporting Stressed Students During the Coronavirus Pandemic, Ramon Barba: Biography, Contributions & Inventions, Real Estate Hearings, Penalties & Appeals in Delaware, 9th Grade Assignment - Reading Skills Self-Assessment, Analyzing Technological System Barriers to Healthcare Delivery & Coordination, Quiz & Worksheet - Situational Crime Prevention, Quiz & Worksheet - Paleolithic Period Weapons, Flashcards - Real Estate Marketing Basics, Flashcards - Promotional Marketing in Real Estate, Human Growth & Development Syllabus Resource & Lesson Plans, ORELA Early Childhood Education: Practice & Study Guide, Algebra I Curriculum Resource & Lesson Plans, McDougal Littell World History: Online Textbook Help, Nationalism in Europe, Africa, Asia & the Americas, Quiz & Worksheet - Steps of Translation of mRNA to Protein, Quiz & Worksheet - Process for Digesting Fiber, Quiz & Worksheet - The Lower Gastrointestinal Tract, Quiz & Worksheet - Organizing Informative Speeches, Quiz & Worksheet - Multicellular Organisms, Tissues and Epithelium, Selecting Relevant Support for Your Speech. We can tell that the relationship is directly proportional by looking at the graph. If you know the constant ratio, then you can figure out your points.

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