Let's consider the given pairs of values [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
| [tex]\( x \)[/tex] | -4 | -1 | 0 | 2 | 5 |
|:-------:|:--:|:--:|:-:|:--:|:-:|
| [tex]\( y \)[/tex] |1245| 33 | 5 | 9 |1335|
To approach this problem systematically, we notice that for each specific value of [tex]\( x \)[/tex], there is a corresponding value of [tex]\( y \)[/tex].
1. List out the pairs:
- For [tex]\( x = -4 \)[/tex], [tex]\( y = 1245 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( y = 33 \)[/tex]
- For [tex]\( x = 0 \)[/tex], [tex]\( y = 5 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y = 9 \)[/tex]
- For [tex]\( x = 5 \)[/tex], [tex]\( y = 1335 \)[/tex]
2. Analysing the pairs:
- When [tex]\( x \)[/tex] is negative, [tex]\( y \)[/tex] can be much larger, as noted with [tex]\( x = -4 \)[/tex] resulting in [tex]\( y = 1245 \)[/tex] and [tex]\( x = -1 \)[/tex] resulting in [tex]\( y = 33 \)[/tex].
- When [tex]\( x \)[/tex] is zero, [tex]\( y \)[/tex] is 5.
- Positive [tex]\( x \)[/tex] values result in relatively small [tex]\( y \)[/tex] values except for [tex]\( x = 5 \)[/tex], which gives [tex]\( y = 1335 \)[/tex].
3. Conclusion of pattern recognition:
- The given pairs do not follow a simple arithmetic or geometric sequence.
- The relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is more complex and seemingly non-linear based on the provided values.
In summary, the values in the table represent specific corresponding pairs, and each [tex]\( x \)[/tex] value results in a unique [tex]\( y \)[/tex] value as shown.
