ALGRZ.MATH.3.D

Represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations such as combining a 20% discount and a 6% sales tax on a sale to determine h(x), the total sale, f(x) = 0.8x, g(x) = 0.06(0.8x), and h(x) = f(x) + g(x).

Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
resulting functionarithmetic operationsfunctionstabular representationsgraphical representationssymbolic representations20% discount6% sales taxtotal salef(x)g(x)h(x)
Skills
  • represent (a resulting function using multiple representations) #dok2
  • combine (functions using arithmetic operations) #dok2
  • interpret (real-world problem contexts using function notation) #dok2
  • organize (function values and operations in tables, graphs, and symbols) #dok2
  • explain (how combined functions apply to real-life situations) #dok3
Learning Targets
  • I can represent the result of combining functions using tables, graphs, and symbols. #dok2
  • I can combine functions using addition, subtraction, multiplication, or division as appropriate for a scenario. #dok2
  • I can interpret a real-world scenario and write functions to model different steps of the process. #dok2
  • I can organize and show how two or more functions are used together to solve a problem using a table, graph, or algebraic equation. #dok2
  • I can explain how combining functions reflects multi-step processes in real-life situations. #dok3
  • I can justify my approach to representing and combining functions to solve a real-world problem. #dok3
Big Ideas
  • Combining functions through arithmetic operations allows us to model and solve complex, multi-step real-world problems.
  • Functions can be represented and interpreted in different ways—tables, graphs, and symbols—to provide multiple perspectives and approaches to understanding problems.
Essential Questions
  • How does combining two or more functions model real-life multi-step problems?
  • What are different ways to represent combined functions, and how do these representations help us solve problems?
  • How can you use function notation and arithmetic operations to describe a sequence of operations, such as discounts and taxes?
  • How does changing one function in a combination affect the resulting function and its representation?
  • How do symbolic, tabular, and graphical representations reflect the process of combining functions in context?