CCSS.Math.Content.HSF-BF.B.4d
The standard
(+) Produce an invertible function from a non-invertible function by restricting the domain.
Common Core State Standards for Mathematics · Build new functions from existing functions
What this standard means
Students need to see when a function fails the horizontal line test, then choose a smaller domain where each output comes from only one input. They should be able to state the restricted domain, write the new function, and find or describe its inverse.
Mastery looks like choosing a sensible restriction, often one side of a turning point, and explaining why it works. Students often get stuck thinking any smaller interval works, ignoring endpoints, or forgetting that the inverse switches inputs and outputs.
Ways to teach it
- Hands-on activity: Give students graph cards for x squared, absolute value, and sine, then have them shade a domain that makes each invertible.
- Writing prompt: Explain why y equals x squared is not invertible on all real numbers, but is invertible when x is at least zero.
- Quick assessment: Show f(x)=|x-3| and ask students to choose a domain restriction and write the inverse for that branch.
- Real-world connection: Use height of a thrown ball over time, then restrict to the falling part so one height matches one time.
Plan a lesson for CCSS.Math.Content.HSF-BF.B.4d
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Related standards
- CCSS.Math.Content.HSF-BF.B.4
Find inverse functions.
- CCSS.Math.Content.HSF-TF.B.6
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- CCSS.Math.Content.HSF-BF.B.4c
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
- CCSS.Math.Content.HSF-BF.B.4b
(+) Verify by composition that one function is the inverse of another.