Question

1. does the relation represent a function?

x | -1 | -2 | -3 | -4 | -5
y | -2 | -3 | -4 | -4 | -6
a. yes
b. no

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). It is allowed for different inputs to have the same output, but one input cannot have more than one output.

Step2: Check the x - values and their corresponding y - values

We look at the given table:

• For \(x=-1\), the corresponding \(y = - 2\) (only one \(y\)-value)
• For \(x=-2\), the corresponding \(y=-3\) (only one \(y\)-value)
• For \(x = - 3\), the corresponding \(y=-4\) (only one \(y\)-value)
• For \(x=-4\), the corresponding \(y = - 4\) (only one \(y\)-value)
• For \(x=-5\), the corresponding \(y=-6\) (only one \(y\)-value)

Even though \(x = - 3\) and \(x=-4\) both have \(y = - 4\), this is allowed because different inputs can have the same output. The key is that each input has only one output.

Answer:

A. Yes