Practice question · Sort into groups
A function assigns exactly one output to each input. Sort each correspondence.
Groups: Is a function · Not a function
- To each integer, the constant 7
- To each integer, its square
- To each positive number, a number whose square is it
- To each person, their sibling
- To each person, their date of birth
Hints
- A rule fails if any input has two outputs, or none at all.
- Some people have several siblings; every positive number has two square roots.
Show the answer
Is a function: To each person, their date of birth, To each integer, its square, To each integer, the constant 7
Not a function: To each person, their sibling, To each positive number, a number whose square is it
Why
f2 fails because a person may have several siblings (or none), and f4 fails because 9 maps to both 3 and -3. f5 is a function despite being constant: 'exactly one output' does not require the outputs to differ.
Practise Functions as Mappings
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More questions on Functions as Mappings
- Let f have domain {-2, -1, 0, 1, 2} and rule f(n) = n squared. How many distinct elements are in its image?
- Let f(n) = 2n with domain and codomain the integers. Select every integer that IS in the image of f.
- The rule "send x to its square root" is not a function on the reals, but √x is. What was fixed?
- A function must assign exactly one output to each input. Why does the "exactly one" requirement do more work…
- Order the steps of a proof that f(n) = 3n - 2 is injective.
- Every function from the integers to the integers is surjective.
- Complete the definition of an injective function.