CCSS.Math.Content.HSF-IF.A.1
The standard
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).
Common Core State Standards for Mathematics
What this standard means
Students need to know that a function is a rule where each allowed input has one output. They should connect inputs, outputs, function notation, tables, graphs, and ordered pairs. They also need to read f(x) as the output when the input is x, not as multiplication.
Mastery looks like sorting relations into functions and non-functions, explaining why, and using f(3) or f(a) correctly from a rule, table, or graph. Students often get stuck when one output repeats, when x-values are hidden in a graph, or when function notation feels like a new operation.
Ways to teach it
- Give pairs card sets of tables, graphs, mappings, and ordered pairs, then have them sort into function and not function with a reason.
- Ask students to write: Can two different inputs have the same output in a function, and how do you know?
- Show four small relations and have students circle the non-functions, then write one sentence explaining each choice.
- Use a vending machine example where each button code gives one item, then discuss what would make the machine fail as a function.
Plan a lesson for CCSS.Math.Content.HSF-IF.A.1
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Related standards
- CCSS.Math.Content.HSA-REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); fin...
- CCSS.Math.Content.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.
- CCSS.Math.Content.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input a...
- CCSS.Math.Content.HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.