Question

graph the piece - wise - defined function. g(x)=
{7 if x < - 2
{5 if x >= - 2
choose the correct graph below.

Explanation:

Step1: Analyze the first - part of the piece - wise function

For \(g(x)=7\) when \(x < - 2\), this is a horizontal line \(y = 7\) for all \(x\) values less than \(-2\). The graph will have an open - circle at \(x=-2\) (because \(x=-2\) is not included in this part of the domain).

Step2: Analyze the second - part of the piece - wise function

For \(g(x)=5\) when \(x\geq - 2\), this is a horizontal line \(y = 5\) for all \(x\) values greater than or equal to \(-2\). The graph will have a closed - circle at \(x = - 2\) (because \(x=-2\) is included in this part of the domain).

Answer:

The correct graph is the one where there is a horizontal line \(y = 7\) with an open - circle at \(x=-2\) for \(x < - 2\) and a horizontal line \(y = 5\) with a closed - circle at \(x=-2\) for \(x\geq - 2\). Without seeing the actual options clearly labeled with A, B, C, D details, based on the above description, you should be able to identify the correct one. If we assume the standard way of graphing piece - wise functions in multiple - choice questions, the graph with an open - circle at \((-2,7)\) and a closed - circle at \((-2,5)\) with \(y = 7\) to the left of \(x=-2\) and \(y = 5\) to the right of and including \(x=-2\) is the correct one.