Maryland Math 8.AT.C.6.b

Math8th GradeAlgebraic Thinking

The Standard

8.AT.C.6: Determine whether a relationship is a function by analyzing whether each input is assigned to exactly one output.

Given a graph, identify input-output pairs and determine whether the graph represents a function.

Maryland College and Career Ready Standards for Mathematics (2025) · REASON ABOUT FUNCTIONS.

Teacher's field guide

What Students Need to Do: Students read points on a graph as input-output pairs. They check whether any input has more than one output, then decide if the graph shows a function.
What Mastery Looks Like: Students list pairs from a graph and explain their decision using the input values. They know that two inputs can share an output, but one input cannot have two different outputs.
Common Misconceptions: Students may read a pair backward and treat the output as the input. They may think repeated outputs break the function rule or miss points stacked above the same input.
How to Assess It: Show a graph with points (1, 2), (2, 4), (1, 5), and (3, 4). Ask students to list the pairs and explain whether it shows a function.

Lesson moves

Give pairs a coordinate grid and sticky dots labeled (0, 1), (1, 3), and (1, 4); have them plot and check repeated inputs.
Show an upright U-shaped graph and a sideways U-shaped graph; ask which gives one output for each input and why.
Put four point graphs on cards; have students sort them into function and not function piles and defend each choice.
Graph daily high temperatures for one week, with day number as the input; have students name two pairs and explain why it is a function.

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