CCSS.Math.Content.HSF-BF.B.4c
The standard
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
Common Core State Standards for Mathematics · Build new functions from existing functions
What this standard means
Students need to read an inverse function from a table or graph without finding a full equation. They should know that inverse functions swap inputs and outputs, so if f(3)=7, then f⁻¹(7)=3. On a graph, they need to connect a point on f to the matching reversed point on its inverse.
Mastery looks like using tables, ordered pairs, and graphs to answer inverse value questions quickly and accurately. Students often get stuck by looking for the same x-value, mixing up f and f⁻¹, or assuming every graph has an inverse without checking that outputs are not repeated.
Ways to teach it
- Give pairs a table of f values and have them build the inverse table by swapping each input and output column.
- Prompt students: If f(a)=b, what must f⁻¹(b) equal, and how can you see that in a table?
- Show five inverse value questions from tables and graphs, then have students answer on mini whiteboards in two minutes.
- Use a phone number lookup analogy, where a name gives a number and the inverse lookup starts with the number.
Plan a lesson for CCSS.Math.Content.HSF-BF.B.4c
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Related standards
- CCSS.Math.Content.HSF-BF.B.4
Find inverse functions.
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- CCSS.Math.Content.HSF-BF.B.4b
(+) Verify by composition that one function is the inverse of another.
- CCSS.Math.Content.HSF-BF.B.4d
(+) Produce an invertible function from a non-invertible function by restricting the domain.