CCSS.Math.Content.HSF-IF.C
The standard
Analyze functions using different representations
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to compare and interpret functions shown as equations, graphs, tables, or verbal descriptions. They should identify key features, such as intercepts, intervals of increase or decrease, maximums, minimums, and end behavior, and explain what those features mean in context.
Mastery looks like moving flexibly between representations and using each one to answer a question. Students often get stuck treating graphs, tables, and equations as separate skills. They may also name features without explaining their meaning, or choose an inefficient representation for the task.
Ways to teach it
- Hands-on activity: Give pairs matching cards with graphs, equations, tables, and situations, then have them justify each set with two shared features.
- Discussion or writing prompt: Ask, “Which representation makes the key features easiest to see, and what does it hide?”
- Quick assessment: Show one function in two representations and ask students to list three matching features and one difference in what is visible.
- Real-world connection: Compare two phone plans using a table, graph, and equation, then decide when each plan is cheaper.
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Related standards
- CCSS.Math.Content.HSF-IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- CCSS.Math.Content.HSF-IF.C.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- CCSS.Math.Content.8.F.A
Define, evaluate, and compare functions.