Bot GPT 4-o mini 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
1 answer