Question

9
a set of points representing a relationship is shown:
(0, 2), (1, 3), (2, 10), (3, -6)
which statement correctly describes the relationship?
a the relationship is a function because all the domain values are positive.
b the relationship is not a function because there is a range value that is negative.
c the relationship is a function because each domain value corresponds to exactly one range value.
d the relationship is not a function because there is a range value that is the same as a domain value.

Explanation:

Step1: Recall function definition

A function is a relation where each domain (input) value has exactly one range (output) value.

Step2: Analyze domain values

Given points: \((0, 2)\), \((1, 3)\), \((2, 10)\), \((3, -6)\).
Domain values (x - values): \(0\), \(1\), \(2\), \(3\). Each domain value appears once.

Step3: Evaluate each option

• Option 1: "all domain values positive" is false (0 is not positive). Eliminate.
• Option 2: "not a function" is wrong. The domain - range mapping is unique. Eliminate.
• Option 3: "negative range value" doesn't determine if it's a function. Eliminate.
• Option 4: Each domain value (\(0\), \(1\), \(2\), \(3\)) has exactly one range value (\(2\), \(3\), \(10\), \(-6\)) → satisfies function definition.

Answer:

The relationship is a function because each domain value corresponds to exactly one range value. (The fourth option)