Lesson 3: Domain and Range

What constitutes the domain of a function and what constitutes the range of a function?

Domain: Range

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.

Lesson Description: This lesson focuses on identifying the set of all valid inputs (Domain) and the set of all resulting outputs (Range). Students will move beyond simple lists of numbers to analyzing more complex representations, including: Discrete vs. Continuous Sets: Distinguishing between data that consists of individual points (like a list of ordered pairs) and data that forms a solid line or curve. Graphical Analysis: Finding domain and range by scanning a graph horizontally (for x) and vertically (for y).Interval Notation: Using brackets and parentheses to describe continuous spans of numbers (e.g., $[0, infinity).Practical Constraints: Identifying "reasonable" domains for real-world applications (e.g., why a domain for "number of tickets sold" cannot include negative numbers or fractions).
Purpose: The purpose of Section 7.3 is to teach students to define the scope of a problem. In higher-level mathematics and programming, knowing the domain is essential for avoiding "undefined" errors (like dividing by zero). In a broader sense, this section develops the habit of checking the "reasonableness" of data—understanding that functions often have limits based on the physical world or the constraints of the algebraic rule itself.
Depth of Knowledge (DOK) Level
DOK Level 2 & 3
Level 2 (Skill/Concept): Identifying the domain and range from a variety of graphs and tables. Translating these sets into correct interval notation.
Level 3 (Strategic Thinking): Determining the "practical domain" for a word problem. Students must evaluate a context (e.g., the height of a ball over time) and decide where the domain must logically start and end, even if the algebraic equation could technically continue forever.

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."
Students often confuse the domain and range. Stress the x is before y and d is before r.

Class and online work

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