Question

does the relation shown below define a function?
y = 2x - 3

○ no
○ yes

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). For a linear equation of the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we can analyze the mapping from \(x\) to \(y\).

Step2: Analyze the equation \(y = 2x-3\)

For any given value of \(x\) (input), when we substitute it into the equation \(y = 2x - 3\), we will get exactly one value of \(y\) (output). For example, if \(x = 0\), then \(y=2(0)-3=- 3\); if \(x = 1\), then \(y=2(1)-3=-1\). There is no value of \(x\) for which we will get more than one value of \(y\). So, this relation satisfies the definition of a function.

Answer:

Yes