Question

the domain and range of part of linear function s are given.
x ≤ 3
y ≥ -2
which graph could represent this part of linear function s?

Explanation:

Step1: Analyze domain

The domain is \(x\leq3\), which means the graph should have values of \(x\) only up to and including \(x = 3\). So, the graph should be restricted to the left - hand side of the vertical line \(x=3\) (including the line \(x = 3\) itself).

Step2: Analyze range

The range is \(y\geq - 2\), which means the graph should have values of \(y\) that are greater than or equal to \(-2\). So, the graph should be above the horizontal line \(y=-2\) (including the line \(y = - 2\) itself).

Step3: Check options

Option A has a line that has points with \(y\) - values less than \(-2\), so it is incorrect. Option B has a line that is restricted to \(x\leq3\) and \(y\geq - 2\). Option C has points with \(x>3\), so it is incorrect. Option D has points with \(y < - 2\), so it is incorrect.

Answer:

B