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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students work backward from an output to find the original input. They read that relationship from ordered pairs, tables, or points on a graph.
What Mastery Looks Like
- Students find the input that produced a given output. They use the fact that a point (a, b) on f becomes (b, a) on its inverse.
Common Misconceptions
- Students may treat f⁻¹(x) as 1/f(x) or as a negative exponent. They may also reverse the coordinate order incorrectly or search the wrong axis.
How to Assess It
- Show the table x: 1, 2, 4 and f(x): 7, 9, 12. Ask students to find f⁻¹(9) and explain their choice.
Lesson moves
Ways to Teach It
Give pairs of students coordinate cards from a function, then have them swap each ordered pair to build the inverse relation.
Ask students to explain why a point (3, 8) on f means f⁻¹(8) = 3.
Play an inverse matching game where students pair function table entries with inverse statements such as f⁻¹(14) = 5.
Use a Celsius and Fahrenheit table to identify which temperature input matches a given converted output.
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Printable HSF-BF.B.4c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.B.4c, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.2
Understanding function inputs and outputs in notation supports reading inverse values by reversing which quantity is treated as input.
- CCSS.Math.Content.HSF-IF.A.1
Reading inverse values requires treating outputs as inputs and using function notation, tables, and graphs to connect x-values and y-values.
- CCSS.Math.Content.HSF-IF.B.4
Reading inverse values relies on interpreting graph and table inputs and outputs, then reversing the relationship for the inverse.
Keep exploring
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.
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