CCSS.Math.Content.HSF-BF.B
The standard
Build new functions from existing functions
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to make new functions by changing ones they already know. That includes adding, subtracting, multiplying, dividing, composing functions, and finding inverses when possible. They also need to connect the rule, graph, table, and meaning of the new function.
Mastery looks like choosing the right operation, writing the new rule correctly, and explaining what changed. Students often mix up function notation, especially composition. They may treat f(g(x)) like multiplication, forget domain restrictions, or miss that an inverse only works as a function when outputs are not repeated.
Ways to teach it
- Hands-on activity: Give pairs function cards and operation cards, then have them build the new rule, table, and graph on chart paper.
- Discussion or writing prompt: Ask, How is f(g(x)) different from f(x) times g(x), and how can a graph prove it?
- Quick assessment: Give f(x)=2x+3 and g(x)=x squared, then ask for f+g, fg, f(g(x)), and g(f(x)).
- Real-world connection: Use a taxi fare function and a sales tax function, then ask students to write a composite function for total cost.
Plan a lesson for CCSS.Math.Content.HSF-BF.B
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSF-BF.A.1b
Combine standard function types using arithmetic operations.
- 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.
- CCSS.Math.Content.HSF-IF.C
Analyze functions using different representations