Lesson 2: Function Notation

If the function f is defined such that is contains the ordered pair (3, 5), what is f(3)?

Ordered pair; Function; Functional Notation, Input; Output

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 introduces the syntax and evaluation of Function Notation. Students will learn that f(x) is not "f times x," but rather a label that identifies the dependent variable as a function of the independent variable x. Key skills include: Evaluating Functions: Substituting numerical values into a function (e.g., finding f(3) given f(x) = 2x + 5).Variable Substitution: Substituting algebraic expressions into functions (e.g., finding f(a) or f(x+1)).Reading Graphs with Notation: Identifying function values from a graph (e.g., "Given the graph of f, what is the value of f(2)?").Translating Equations: Converting traditional x, y equations into function form.
Purpose: The purpose of Section 7.2 is to develop mathematical precision and shorthand. Function notation allows mathematicians to name different relationships (like f(x) for "fuel" and c(x) for "cost") within the same problem without confusion. It also explicitly links the input and output in one statement—where the coordinates (3, 11) are condensed into the expressive f(3) = 11. Mastering this notation is a non-negotiable prerequisite for Intermediate Algebra and Calculus, where functions are manipulated as individual units.
Depth of Knowledge (DOK) Level
DOK Level 1 & 2
Level 1 (Recall & Reproduction): Evaluating a linear function by substituting a number for the variable. Recognizing the parts of the notation (input, output, and function name).
Level 2 (Skill/Concept): Interpreting f(x) values from a provided graph or table. Students must distinguish between "find f(3)" (where the input is known) and "find x if f(x) = 3" (where the output is known). This requires a conceptual understanding of the roles of x and y within the notation.

The distance a car travels from when the brakes are applied to the car's complete stop is the stopping distance. This includes time for the driver to react. The faster a car is traveling the longer the stopping distance. The stopping distance is a function of the speed of the car.

Function notation is sometimes difficult for student to comprehend. Stress that f(x) does not mean "f times x."

Class and online work

Use practice problems 5-12, page 168-170 to assess students' understanding of the lesson concepts