Question

Which of the following relations is a one-to-one function?(1 point) Responses {(−3,−2),(3,4),(−1,−2),(−1,5)} start set open paren negative 3 comma negative 2 close paren comma open paren 3 comma 4 close paren comma open paren negative 1 comma negative 2 close paren comma open paren negative 1 comma 5 close paren end set {(1,2),(1,4),(1,5),(1,6)} start set open paren 1 comma 2 close paren comma open paren 1 comma 4 close paren comma open paren 1 comma 5 close paren comma open paren 1 comma 6 close paren end set {(4,−5),(3,−5),(2,8),(1,8)} start set open paren 4 comma negative 5 close paren comma open paren 3 comma negative 5 close paren comma open paren 2 comma 8 close paren comma open paren 1 comma 8 close paren end set {(10,9),(8,7),(6,5),(4,3)}

explain how do you know?

in a short way

Answer 1

A one-to-one function (or injective function) is defined such that each input maps to a unique output; no two different inputs can map to the same output.

Let's analyze the given relations:

1. **{(−3,−2), (3,4), (−1,−2), (−1,5)}:** The input -1 maps to both -2 and 5. **Not one-to-one.**

2. **{(1,2), (1,4), (1,5), (1,6)}:** The input 1 maps to multiple outputs (2, 4, 5, 6). **Not one-to-one.**

3. **{(4,−5), (3,−5), (2,8), (1,8)}:** The inputs 4 and 3 both map to -5, and 2 and 1 both map to 8. **Not one-to-one.**

4. **{(10,9), (8,7), (6,5), (4,3)}:** All inputs map to unique outputs (10 to 9, 8 to 7, 6 to 5, 4 to 3). **This is one-to-one.**

**Conclusion:** The relation **{(10,9), (8,7), (6,5), (4,3)}** is the only one that is a one-to-one function.