CCSS.Math.Content.HSF-IF.B.5
The standard
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Common Core State Standards for Mathematics
What this standard means
Students need to connect allowed input values to both the graph and the situation. They should decide whether inputs can be all real numbers, only positives, whole numbers, or a limited interval. They also need to explain why certain x-values make no sense in context.
Mastery looks like choosing a reasonable domain from a story, showing it on a graph, and justifying it with units and meaning. Students often graph a full line or curve because the equation allows it, then forget the context. They also mix up discrete inputs, like number of tickets, with continuous inputs, like time or distance.
Ways to teach it
- Give groups equation cards and context cards, then have them match each to a graph with the correct domain shaded or marked.
- Ask students to write: What x-values does the equation allow, and what x-values does the situation allow?
- Show three graphs for one situation, and have students circle the one with the correct domain and explain one rejected choice.
- Use a pricing plan, concert tickets, or gallons of gas example, and have students list possible input values before graphing.
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