CCSS.Math.Content.HSF-IF.A.3
The Standard
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect each term number to exactly one term value. They read sequences as functions with selected integer inputs and generate terms from recursive rules.
What Mastery Looks Like
- Students can represent a sequence with ordered pairs, a table, or function notation. They can use a recursive rule to generate terms and state which integer inputs are allowed.
Common Misconceptions
- Students may treat the term number as the term value. They may use every real number as an input or apply a recursive rule without finding earlier terms first.
How to Assess It
- Give the sequence a(1) = 5 and a(n) = 2a(n-1) - 1. Ask students to list four terms, state the domain, and explain why it is a function.
Lesson moves
Ways to Teach It
Give groups numbered index cards and value cards, then have them build a sequence and display it as ordered pairs.
Ask students to explain why a sequence can be a function even though its graph is separate points.
Run a recursive sequence relay where each student calculates one term, checks the previous term, and passes the result onward.
Model weekly savings with a starting amount and fixed increase, then identify the week numbers as the function's domain.
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Printable HSF-IF.A.3 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-IF.A.3, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.1
Recognizing sequences as functions requires knowing functions pair each allowed input with exactly one output and have a domain.
- CCSS.Math.Content.8.F.A.1
Students need the one-input, one-output function idea to see each term number in a sequence as producing one term value.
- CCSS.Math.Content.HSF-IF.A.2
Function notation and evaluating inputs carry over to treating term numbers as inputs and sequence terms as function values.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- 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.4d
(+) Produce an invertible function from a non-invertible function by restricting the domain.
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