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Hong KongFunctions, and what the rule says about patterns
Skill 6 reads "Identify relations that satisfy the definition of a function". A relation is a function when every input has exactly one output. Sequences and number patterns are not named anywhere in the twenty-one Mathematics skills, so treat them as background rather than a topic.
Two things in this post's title, and the rule treats them very differently. Functions get a skill of their own. Sequences get nothing.
The definition, and the three ways it is tested
A relation is a function when every input has exactly one output. That is the whole definition and everything else is a way of checking it.
| Presentation | The check | What fails |
|---|---|---|
| A graph | Vertical line test | Any vertical line crossing the curve twice |
| A table | Look for repeated inputs | The same x with two different y values |
| A set of ordered pairs | Look at first coordinates | A first coordinate appearing twice with different partners |
| A mapping diagram | Count arrows leaving each input | An input with two arrows |
Repeated outputs are fine. Two different inputs can share an output and the relation is still a function, which is the point candidates most often get backwards.
Which set of ordered pairs represents a function?
- (1, 4), (2, 5), (1, 6), (3, 7)
- (1, 4), (2, 4), (3, 4), (4, 4)
- (2, 1), (2, 3), (4, 5), (6, 7)
- (0, 1), (0, 2), (1, 3), (1, 4)
Function notation
The notation f of x is a name for the output when the input is x. Evaluating it is substitution: if f of x equals 2x plus 3, then f of 4 is 11.
The rule does not name function notation as a skill. It appears here because an item testing skill 6 or skill 7 may use it, and being thrown by the notation is a bad way to lose a question you could otherwise answer.
What the rule does not say
Search the twenty-one Mathematics skills for sequence, pattern, arithmetic sequence, geometric sequence or nth term. None of them appears.
That is genuinely useful information. Sequence questions are a staple of general mathematics tests and of most prep material, and Florida's rule does not name them. If a study product spends a chapter on the nth term of an arithmetic sequence, it is working from a generic syllabus rather than from Section 82.
Where a pattern could still appear
Inside skill 5, which asks you to use data to plot points and determine additional solutions. A table of values with a constant difference is a linear pattern, and finding the next value is finding another solution.
So the skill is really linearity rather than sequences. If the differences between consecutive values are constant, you have a straight line, and the constant difference is the slope. That single observation covers everything a pattern question at this level could reasonably ask.
What we would spend on this
Twenty minutes on the definition of a function and the vertical line test. Ten minutes on function notation so it does not startle you. Nothing on sequences beyond noticing constant differences.
The concession: skill 6 is one of seven in a competency we estimate at about 12 of the 35 questions, and our estimate is arithmetic on the rule's skill counts rather than a published weighting. It may be one item. It is a cheap item, and cheap items are how a subtest that passes at about 22 of 35 gets won.
Common questions
What makes a relation a function on the FTCE?
Every input has exactly one output. Repeated outputs are fine; repeated inputs with different outputs are not. That single sentence covers the vertical line test, the table check and the ordered-pair check, which are three presentations of the same idea.
Are sequences tested on the FTCE General Knowledge Test?
No skill in Section 82 mentions sequences, patterns or the nth term. Prep material that devotes a chapter to arithmetic and geometric sequences is following a generic mathematics syllabus rather than the competencies Florida incorporated into its rule.
Do I need function notation?
It is not a named skill, but an item testing functions or comparing linear functions may use it. Evaluating f of x is just substitution: if f of x equals 2x plus 3, then f of 4 is 11. Ten minutes of familiarity is enough.
Can two inputs share the same output?
Yes, and the relation is still a function. A set of pairs where every output is the same value is a perfectly good function, which is why that option catches candidates who have remembered the rule in the wrong direction.