ALGRZ.MATH.3.E
Model a situation using function notation when the output of one function is the input of a second function such as determining a function h(x) = g(f(x)) = 1.06(0.8x) for the final purchase price, h(x) of an item with price x dollars representing a 20% discount, f(x) = 0.8x followed by a 6% sales tax, g(x) = 1.06x.
Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
function notationoutputinputfunctionsituationfinal purchase priceitempricedollarsdiscountsales tax
Skills
- model (real-world situations using function notation) #dok2
- determine (output of a composition of functions) #dok2
- interpret (functions in context of discounts and taxes) #dok2
- represent (function composition symbolically) #dok1
- analyze (relationships between composed functions and real-world contexts) #dok3
Learning Targets
- I can represent the output of one function as the input of a second function using function notation. #dok1
- I can determine the final value in real-world situations by composing two or more functions. #dok2
- I can model real-world problems, such as calculating final price after discounts and taxes, by composing functions using function notation. #dok2
- I can interpret the meaning of a composed function in the context of a real-life scenario. #dok2
- I can analyze and explain how function composition represents sequential changes in real-world contexts. #dok3
Big Ideas
- Composing functions allows us to model and solve multi-step real-world problems efficiently using mathematical notation.
- Function notation provides a powerful way to connect real-life processes, such as discounts and taxes, into a systematic calculation.
Essential Questions
- How can function notation be used to represent multi-step real-world situations?
- What does it mean when the output of one function becomes the input of another?
- How does composing functions help in modeling problems with multiple sequential changes, such as applying a discount then a tax?
- In what ways can we interpret the meaning of composed functions in real-life scenarios?
- How can understanding function composition help us solve practical problems more efficiently?