Question

graph the piecewise - defined function.
g(x)=\left\\{\

$$\begin{array}{ll}3 & \\text { if } x<-2 \\\\ 2 & \\text { if } x \\geq-2\\end{array}$$

\
ight.
choose the correct graph below.

Explanation:

Step1: Analyze the piece - wise function for \(x < - 2\)

For \(x < - 2\), \(g(x)=3\). This is a horizontal line \(y = 3\) for all \(x\) values less than \(-2\).

Step2: Analyze the piece - wise function for \(x\geq - 2\)

For \(x\geq - 2\), \(g(x)=2\). This is a horizontal line \(y = 2\) for all \(x\) values greater than or equal to \(-2\).

Step3: Check the point at \(x=-2\)

When \(x = - 2\), we use the second part of the piece - wise function \(g(x)=2\). So the point \((-2,2)\) is a solid point (since the inequality is \(x\geq - 2\)), and for \(x < - 2\), the line \(y = 3\) has an open - circle at \(x=-2\) (since \(x=-2\) is not included in the \(x < - 2\) part).

Answer:

Assuming option A has a solid point at \((-2,2)\) and a horizontal line \(y = 3\) for \(x < - 2\) (with an open - circle at \(x=-2\) for the \(y = 3\) part) and \(y = 2\) for \(x\geq - 2\), option A is the correct graph.