Which of these describes f : Z → Z, f(n) = n + 3?

Relations & Functions · Question 99 of 125

Question 99

EasyOriginal question

Which of these describes $f : \mathbb{Z} \to \mathbb{Z}$ , $f(n) = n + 3$ ?

One-one but not ontoCorrect answerYour answerOne-one and ontoCorrect answerYour answerOnto but not one-oneCorrect answerYour answerNeither one-one nor ontoCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$a + 3 = b + 3$ gives $a = b$ : one-one.
Any integer $m$ is $f(m - 3)$ , and $m - 3$ is an integer: onto.

Worth noting

On $\mathbb{Z}$ there is always a number 3 below; on $\mathbb{N}$ there would not be.

Concept: Classifying a function
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsOnto and bijective functions

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Which of these describes f:Z→Zf : \mathbb{Z} \to \mathbb{Z}f:Z→Z, f(n)=n+3f(n) = n + 3f(n)=n+3?

Explanation

Which of these describes $f : \mathbb{Z} \to \mathbb{Z}$ , $f(n) = n + 3$ ?