Question

Which table show y as a function of x?
a x: -13,-13,-13,-13 y: -2,0,5,7
b x: -6,-1,-1,10 y: 3,-1,5,-9
c x: 1,3,7,12 y:4,4,4,4
d x: -9,-2,0,0 y: -7,-5,0,6

Answer 1

To determine which table represents \( y \) as a function of \( x \), we need to look for a rule that assigns each input \( x \) to exactly one output \( y \). In other words, each value of \( x \) must correspond to only one value of \( y \).

Let's examine each option:

a)
- \( x: -13, -13, -13, -13 \)
- \( y: -2, 0, 5, 7 \)

Here, the same \( x \) value (-13) has different \( y \) values. This does not satisfy the definition of a function.

b)
- \( x: -6, -1, -1, 10 \)
- \( y: 3, -1, 5, -9 \)

In this case, the same \( x \) value (-1) has different \( y \) values (5 and -1). This also does not satisfy the definition of a function.

c)
- \( x: 1, 3, 7, 12 \)
- \( y: 4, 4, 4, 4 \)

Here, every \( x \) has the same \( y \) value of 4. Each \( x \) corresponds to exactly one \( y \) value, satisfying the definition of a function.

d)
- \( x: -9, -2, 0, 0 \)
- \( y: -7, -5, 0, 6 \)

In this case, the same \( x \) value (0) has different \( y \) values (0 and 6). This does not satisfy the definition of a function.

**Conclusion:** The correct choice where \( y \) is a function of \( x \) is **c**.