Lesson 3: Formulas in Functional Notation - Applications

How is the input to a function provided? What does it mean for a function to be equal to a value?

Formula
Function
Input
Output
Independent
Dependent

F.IF.1
A. Understand the concept of a function and use function notation
1. HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of
the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the
equation y = f(x).

2. HSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

B. Interpret functions that arise in applications in terms of the context
5. HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.?

Lesson Description: This lesson focuses on the application of linear functions to describe real-life situations. Students will work with word problems that require them to build, evaluate, and interpret functions. Key activities include: Modeling from Scenarios: Building a function f(x) from a verbal description of a situation (e.g., "The height of a candle h(t) after t hours").Input vs. Output Problem Solving: Using the notation to solve two distinct types of questions :Finding the Result: Given an input, find the output (e.g., "Calculate h(3) to find the height after 3 hours").Finding the Threshold: Given an output, find the input (e.g., "Find t so that h(t) = 0 to determine when the candle burns out").Unit Analysis: Interpreting the meaning of the result in context, ensuring that labels (dollars, hours, feet) are correctly applied. Comparing Models: Using function notation to compare two different options (e.g., P_1(x) and P_2(x) for two different phone plans) to find the "break-even" point.
Purpose: The purpose of Section 8.2 (Applications) is to develop analytical fluency. In a professional setting, data is rarely presented as a simple equation; it is presented as a set of conditions. By using function notation to model these conditions, students learn to organize complex information logically. This section is specifically designed to prepare students for the "Word Problem" heavy nature of MAT 137 and to provide them with the quantitative skills used in the Middlesex CC business and social science tracks.
Depth of Knowledge (DOK) Level
DOK Level 3
Level 3 (Strategic Thinking & Complex Reasoning): This is high-level application. Students aren't just calculating; they are modeling. They must choose the correct mathematical structure to represent a situation, determine whether they are solving for the input or the output, and then explain the real-world significance of their numerical answer. It requires them to justify their process and verify that their answer falls within the "practical domain" they learned about in Chapter 7.

Class and online work

Use "you try" pg 184 and practice problems to assess students' understanding of the lesson concepts