CCSS.Math.Content.HSF-IF.C.9
The standard
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Common Core State Standards for Mathematics
What this standard means
Students need to compare two functions even when they are shown in different forms, such as an equation, graph, table, or story. They should identify features like intercepts, rate of change, maximum or minimum, increasing or decreasing intervals, and end behavior, then use those features to answer a clear comparison question.
Mastery looks like translating each representation into the same kind of information before deciding. Students often get stuck reading graph scale, finding key points from equations, or comparing only outputs without noticing the input values. They may also assume a table shows the whole function, not just sample points.
Ways to teach it
- Give pairs of function cards in mixed forms, and have students sort them by greater y-intercept, faster growth, or higher maximum.
- Ask students to explain which function wins a race to 100 and support the claim using the graph, table, or equation.
- Show one graph and one equation, then ask students to write one correct comparison statement and one piece of evidence.
- Compare two phone plans, one shown in a table and one as an equation, and decide which is cheaper for different data amounts.
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Related standards
- 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.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or ...
- 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.