A rule or set of pairs linking inputs to outputs.

Name four ways to show a relation.

Mapping diagram, table, ordered pairs, graph.

A relation where every input has exactly one output.

Can two different inputs share the same output in a function?

Yes. Only an input with two outputs breaks the rule.

Is 1\to4, 3\to5, 3\to6 a function?

No: the input 3 has two outputs.

What is the vertical line test?

If any vertical line crosses a graph more than once, it is not a function.

What does f(x)=3x-4 mean?

The output is 3x-4 when the input is x.

What is the difference between f(8) and f(x)=8?

f(8): input 8, find the output. f(x)=8: output 8, find the input.

In C(d)=5+2d, what does C(0)=5 mean?

The fixed starting charge is 5 (the cost when the distance is 0).

Relations, mappings and function notationIB MYP Maths Standard: Flashcards

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What is a relation?

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What is a relation?: A rule or set of pairs linking inputs to outputs.
Name four ways to show a relation.: Mapping diagram, table, ordered pairs, graph.
What is a function?: A relation where every input has exactly one output.
Can two different inputs share the same output in a function?: Yes. Only an input with two outputs breaks the rule.
Is $1\to4$ , $3\to5$ , $3\to6$ a function?: No: the input $3$ has two outputs.
What is the vertical line test?: If any vertical line crosses a graph more than once, it is not a function.
What does $f(x)=3x-4$ mean?: The output is $3x-4$ when the input is $x$ .
Find $f(5)$ if $f(x)=3x-4$ .: $3(5)-4=11$
Find $g(-3)$ if $g(x)=x^2+1$ .: $(-3)^2+1=10$
How do you solve $f(x)=8$ for $f(x)=3x-4$ ?: Solve $3x-4=8$ , so $x=4$ .
What is the difference between $f(8)$ and $f(x)=8$ ?: $f(8)$ : input $8$ , find the output. $f(x)=8$ : output $8$ , find the input.
In $C(d)=5+2d$ , what does $C(0)=5$ mean?: The fixed starting charge is 5 (the cost when the distance is 0).

Exam questions on Relations, mappings and function notation

A function is defined by $f(x)=3x-4$ .
Find $f(2a)$ , giving your answer in its simplest form.2 marks
Two relations are given as mappings. Relation $R$ maps $1\to4$ , $2\to5$ , $3\to5$ and $3\to6$ . Relation $S$ maps $1\to4$ , $2\to5$ , $3\to5$ and $4\to5$ .
Change one pair in $R$ so that it becomes a function, and explain why your new relation is a function.2 marks
A taxi company in Doha charges according to the rule $C(d)=5+2d$ , where $C(d)$ is the cost in Qatari riyals (QAR) of a journey of $d$ kilometres.
(i) Find $C(12)$ . (ii) Solve $C(d)=33$ and state what your answer means.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).