Lesson 2: Formulas in Functional Notation

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 bridges the gap between geometry/business formulas and the formal function notation used in higher mathematics. Students will practice: Evaluating Formulas with Notation: Using the f(x) syntax to find specific values (e.g., finding C(10) for a cost function C(x) = 5x + 100).

Purpose: The purpose of Section 8.2 is to standardize mathematical communication. While y = 2x + 1 and f(x) = 2x + 1 produce the same graph, function notation allows for greater clarity when dealing with multiple models simultaneously. This section prepares students for the rigorous notation requirements of MAT 137 and laboratory sciences, where tracking exactly which input (x) led to which output (y) is essential for data integrity and error analysis.

DOK Level 2
Level 2 (Skill/Concept): Students must perform a two-step cognitive process: first, they must correctly substitute a value into a multi-variable formula, and second, they must use the proper notation to report the result. It requires moving beyond simple calculation to understanding the structure of the notation—knowing that A(5) refers to the result of the formula when the radius is 5, rather than a variable "A" multiplied by 5.

Class and online work

Use "you try" pg 182 and practice problems to assess students' understanding of the lesson concepts