CCSS.Math.Content.HSF-BF.A.1

MathGrades 9–12Building Functions

The standard

Write a function that describes a relationship between two quantities

Common Core State Standards for Mathematics

What this standard means

Students need to turn a situation, table, graph, or verbal rule into a function. They choose variables, decide what depends on what, write a rule, and state a reasonable domain. They may use linear, quadratic, exponential, or piecewise forms, depending on the relationship.

Mastery looks like matching the function type to the pattern and explaining what each part of the rule means. Students often get stuck choosing independent and dependent variables, using function notation correctly, and including constraints from the context, such as whole numbers or maximum values.

Ways to teach it

  • Hands-on: Give pairs cup-stacking data, have them measure height for 1 to 8 cups, then write a function for stack height.
  • Prompt: Describe a phone plan with a startup fee and monthly charge, then write and explain a function for total cost.
  • Quick check: Show a table of values and ask students to write f(x), name the function type, and state the domain.
  • Real-world link: Use a rideshare fare card and have students write a function using base fare plus cost per mile.

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Related standards

  • CCSS.Math.Content.HSF-BF.A

    Build a function that models a relationship between two quantities

  • CCSS.Math.Content.HSF-IF.B.4

    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...

  • CCSS.Math.Content.8.F.B.4

    Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of...

  • CCSS.Math.Content.8.F.B

    Use functions to model relationships between quantities.

Standard text verified against corestandards.org on July 10, 2026.

Page updated July 10, 2026.

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