To determine if the given situation is a function, we need to understand what defines a function in the context of a relation between two sets of numbers.
A function is a relation where each input (from the domain) is associated with exactly one output (from the range). In simpler terms, in a function, each input value must correspond to one and only one output value.
Given the table:
| Seconds, [tex]\( x \)[/tex] | Meters, [tex]\( y \)[/tex] |
|-------------------|-----------------|
| 0.5 | 28 |
| 1 | 48 |
| 1.5 | 60 |
| 2 | 64 |
| 2.5 | 60 |
| 3 | 48 |
| 3.5 | 28 |
We need to verify if each input [tex]\( x \)[/tex] (Seconds) has exactly one corresponding output [tex]\( y \)[/tex] (Meters).
Let's examine the pairs:
- For [tex]\( x = 0.5 \)[/tex], [tex]\( y = 28 \)[/tex]
- For [tex]\( x = 1 \)[/tex], [tex]\( y = 48 \)[/tex]
- For [tex]\( x = 1.5 \)[/tex], [tex]\( y = 60 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( y = 64 \)[/tex]
- For [tex]\( x = 2.5 \)[/tex], [tex]\( y = 60 \)[/tex]
- For [tex]\( x = 3 \)[/tex], [tex]\( y = 48 \)[/tex]
- For [tex]\( x = 3.5 \)[/tex], [tex]\( y = 28 \)[/tex]
Upon checking each pair, we observe that each value of [tex]\( x \)[/tex] (input) maps to one and only one value of [tex]\( y \)[/tex] (output). For example, at [tex]\( x = 0.5 \)[/tex] seconds, the height [tex]\( y \)[/tex] is precisely 28 meters and not any other value. This pattern holds true for all mentioned seconds.
Since each input has exactly one corresponding output, we conclude that:
Yes, the situation is a function because each input has exactly one output.
