All functions are regarded as relations. However, not all relations are regarded as functions
The statement is just a function; not just a relation.
The points from the statement are:
- Student's test grade
- Time spent on practice
This means that the test grade is dependent on the amount of time, the student practice.
If a student practices for (say) 10 minutes, his test grade will be (say) 70%
Using the assumed values above; no other student can have a score of 70%, unless the student practices for 10 minutes.
This type of relation is called a many-to-one relation.
A many-to-one relation is not just a relation, it is also a function.
Consider the following many-to-one ordered pair:
[tex](x_1,y_1) \to (10, 70\%)[/tex]
[tex](x_2,y_2) \to (15, 75\%)[/tex]
[tex](x_3,y_3) \to (20, 85\%)[/tex]
[tex](x_4,y_4) \to (40, 100\%)[/tex]
[tex](x_1,y_1) \to (10, 75\%)[/tex]
Hence, the statement is a function.
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