Functions Start Here

Overview

Students are introduced to functions as machines that assign each input exactly one output. They learn function notation, evaluate functions from definitions/graphs, and connect domain and range to real contexts.

Learning intentions

Students will be able to:

• Explain what makes a relation a function (one output for each input).
• Identify the domain and range from a table, mapping, or context.
• Use function notation to interpret inputs and outputs.
• Evaluate a function for given input values and describe the meaning in context.

Success criteria

I can …

• Tell whether a set of ordered pairs or a mapping is a function by checking the “exactly one output” rule.
• Write and read function notation such as f(x) and interpret it as an output.
• Find f(2), f(−1), etc. from a table or rule and explain what it means.
• Describe key features from a simple graph by stating which x-values are allowed (domain) and what y-values occur (range).

Curriculum links

• Functions - Interpreting Functions: Understand a function assigns exactly one output to each domain input.
• Functions - Interpreting Functions: Relate domain to a function’s graph and to the quantities in context.
• Functions - Interpreting Functions: Use function notation and evaluate functions for inputs in the domain.
• Functions - Interpreting Functions: Interpret statements using function notation in context.

Lesson structure (50 minutes)

1. 0–5 min · Hook (Mapping vs. Not a Function). Teacher displays two input-output maps on the board (Map A and Map B). Students decide silently: “Function?” then justify with a one-sentence reason.
2. 5–14 min · Direct teach (What is a function?). Teacher models a function as a “rule/machine” that takes an input x and produces exactly one output f(x), emphasizing “exactly one” and “input must be in the domain.” Students follow along by recording the one-rule definition in their notes and completing two quick yes/no checks.
3. 14–22 min · Function notation and meaning. Teacher introduces notation f(x): the output corresponding to input x, and demonstrates how to read statements like “f(3) = 10” as “the output when x = 3 is 10.” Students practice by matching 4 statements to their meanings (e.g., “f(−2)” to “output when input is −2”).
4. 22–33 min · Guided practice (Evaluate from tables/rules). Teacher provides a table for a function g with a clear domain (for example, g(x) values for x = 0, 1, 2, 3). Students work in pairs (teacher rotates through the small group) to compute outputs like g(2), g(0), and then write a sentence interpreting each output in context (example context: “g(x) is the cost…”). Teacher checks for correct notation and interpretation.
5. 33–41 min · Domain and range connection (table/mapping). Teacher asks: “Which x-values are in the domain? Which outputs occur in the range?” Students highlight the domain and range from the same table/map, then answer a prompt: “If x = 5 is not listed, what does that mean about the function?” Teacher reinforces that not all numbers belong to the domain.
6. 41–48 min · Quick graph check (light introduction). Teacher shows a simple scatter plot/graph with plotted points connected lightly or just a set of points, stating it represents a function. Students verify it passes the one-output test for several x-values and identify the domain and range from the plotted points.
7. 48–50 min · Exit ticket (individual). Students complete: (1) Decide if a provided mapping is a function and explain in 1–2 sentences, (2) Evaluate f(3) from a short table/rule, (3) Write what f(3) means in context.

Resources

• Board/markers or slides with Map A vs. Map B
• Function table handout (teacher-prepared)
• Mapping diagram cards (function and not-a-function)
• Graph image (simple set of points) for domain/range practice
• Student notebooks or graph paper
• Exit ticket slips (1 per student)
• Calculator not needed

Assessment

• Teacher observation during the hook and guided practice: listens for correct “exactly one output” reasoning.
• Spot checks during notation practice: students correctly label inputs/outputs and use f(x) accurately.
• Exit ticket results: quick scoring for (a) function/non-function justification, (b) correct evaluation, (c) accurate domain/range or interpretation sentence.

Differentiation

• Support:
• Provide sentence starters such as “This is a function because each input has ___ output,” and “f(3) means ___.”
• Use color-coding on the table: input column highlighted, output column highlighted.
• Allow students to verbalize the rule before writing notation.
• Extension:
• Ask a “what if” question: “If an input repeats with a different output, what happens to the function?” Students explain using the definition.
• EAL/SEN considerations:
• Keep wording consistent: “input,” “output,” “domain,” “range,” “exactly one.”
• Offer a small word bank on the exit ticket (domain, range, output, input, notation).
• Grouping:
• Since class size is 6, use brief whole-group instruction with frequent checks, then pair students for table evaluation while teacher provides targeted feedback.

Extension (optional)

• SKIP