Question

this table shows data points. what missing values would make the data set a function? a. x = 7, y = 9 b. x = 3, y = 10 c. x = 5, y = 10 d. x = 1, y = 7

Explanation:

Step1: Recall function definition

A relation is a function if for each input (x - value) there is exactly one output (y - value).

Step2: Analyze each option

• Option A: If \(x = 7,y = 9\), when \(x = 7\) appears twice with the same \(y - value\), it's still a function, but we need to check all.
• Option B: If \(x = 3,y = 10\), then \(x = 3\) has two different \(y - values\) (7 and 10), so it is not a function.
• Option C: If \(x = 5,y = 10\), since \(x = 5\) is a new input with a single output, it makes the relation a function.
• Option D: If \(x = 1,y = 7\), then \(x = 1\) has two different \(y - values\) (5 and 7), so it is not a function.

Answer:

C. \(x = 5,y = 10\)