CCSS.Math.Content.HSF-BF.A.1c
The standard
(+) Compose functions.
Common Core State Standards for Mathematics · Build a function that models a relationship between two quantities
What this standard means
Students need to combine two functions so the output of one becomes the input of the other. They should be able to write composite functions using notation like f(g(x)), explain what the new input and output mean, and use tables, graphs, equations, or contexts to find values.
Mastery looks like choosing the correct order and interpreting the result in context, not just doing algebra. Students often reverse the order, plug into the wrong function first, or ignore domain limits. Contexts help reveal whether the composition makes sense.
Ways to teach it
- Hands-on activity: Give pairs two function machines with input-output cards, then have them pass outputs from one machine into the next and record f(g(x)).
- Prompt: Explain in words the difference between C(m(t)) and m(C(t)) for a car cost function and a miles-over-time function.
- Quick assessment: Give f(x)=2x+3 and g(x)=x^2, then ask students to find f(g(4)), g(f(4)), and one domain concern.
- Real-world connection: Model phone battery percent as a function of screen time, then screen time as a function of hours since unplugging.
Plan a lesson for CCSS.Math.Content.HSF-BF.A.1c
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