Question

Which relation(s) best shows y as a function of x?
select all that apply
a {(01,2), (3,-4), (-1,7),(0,9)}
b {(1,6), (3,4),(-1,3),(0,-5)}
c {(1,2),(3,2),(-1,2),(0,2)}
d {(-5,8),(8,4),(-2,5),(0,-4)}
e {(1,7),(3,4),(1,-3),(2,-6)}
f {(9,2),(0,-4),(-1,6),(9,-8)}

Answer 1

To determine which relations represent \( y \) as a function of \( x \), we need to ensure that for every \( x \) value in the relation, there is exactly one corresponding \( y \) value. In other words, no two pairs in the relation can have the same \( x \) value with different \( y \) values.

Let's evaluate each relation:

a) \(\{(0,2), (3,-4), (-1,7),(0,9)\}\)
- The \( x \) value \( 0 \) corresponds to two different \( y \) values: \( 2 \) and \( 9 \).
- **Not a function.**

b) \(\{(1,6), (3,4),(-1,3),(0,-5)\}\)
- All \( x \) values are unique.
- **Is a function.**

c) \(\{(1,2),(3,2),(-1,2),(0,2)\}\)
- All \( x \) values are unique.
- **Is a function.**

d) \(\{(-5,8),(8,4),(-2,5),(0,-4)\}\)
- All \( x \) values are unique.
- **Is a function.**

e) \(\{(1,7),(3,4),(1,-3),(2,-6)\}\)
- The \( x \) value \( 1 \) corresponds to two different \( y \) values: \( 7 \) and \( -3 \).
- **Not a function.**

f) \(\{(9,2),(0,-4),(-1,6),(9,-8)\}\)
- The \( x \) value \( 9 \) corresponds to two different \( y \) values: \( 2 \) and \( -8 \).
- **Not a function.**

In summary, the relations that show \( y \) as a function of \( x \) are:

- **b**
- **c**
- **d**