Question

does the following data represent a function?
x| 2 0 2 5
y| 1 -3 1 22

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). In other words, no two ordered pairs can have the same x - value with different y - values.

Step2: Analyze the given x - values

We look at the x - values in the table: 2, 0, 2, 5. The x - value 2 appears twice.

Step3: Check the corresponding y - values for the repeated x - value

When \(x = 2\), the first time \(y=1\) and the second time \(y = 1\) as well. So even though the x - value 2 is repeated, the corresponding y - value is the same in both cases. Let's list out the ordered pairs: \((2,1)\), \((0, - 3)\), \((2,1)\), \((5,22)\). For a function, we just need that each x has a unique y (it's okay if different x's have the same y). Here, the x - value 2 always maps to y = 1, x = 0 maps to y=-3, and x = 5 maps to y = 22. So each x - value has exactly one y - value.

Answer:

Yes, the data represents a function. Because even though the x - value 2 is repeated, it maps to the same y - value (1) in both cases, and each other x - value (0 and 5) also maps to a unique y - value. So each input (x - value) has exactly one output (y - value), which satisfies the definition of a function.