Question

consider the graphed function.
what are the domain and the range of this function?

Explanation:

Step1: Determine the domain

The domain of a function is the set of all possible \(x\)-values. Looking at the graph, the leftmost point (closed dot) is at \(x = -5\), and the rightmost point (open dot) is at \(x = 1\). So the domain is \(-5 \leq x < 1\) (since the closed dot includes \(-5\) and the open dot excludes \(1\)).

Step2: Determine the range

The range of a function is the set of all possible \(y\)-values. The lowest point (closed dot) has a \(y\)-value of \(-4\), and the highest point (open dot) has a \(y\)-value of \(7\). So the range is \(-4 \leq y < 7\) (since the closed dot includes \(-4\) and the open dot excludes \(7\)).

Answer:

Domain: \(-5 \leq x < 1\), Range: \(-4 \leq y < 7\)