Question

sketch the graph of the function using a window that gives a complete graph.

f(x)=left{\begin{array}{cc}-3 & \text { if } x geq 2 \\ 3 & \text { if } x<2end{array}
ight.

choose the correct graph below.

a.
b.
c.
d.

Explanation:

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

When \(x < 2\), \(F(x)=3\). This is a horizontal line \(y = 3\) for all \(x\) values less than \(2\). At \(x = 2\), since \(x<2\) does not include \(x = 2\), there is an open - circle at the point \((2,3)\) for this part of the piece - wise function.

Step2: Analyze the function for \(x\geq2\)

When \(x\geq2\), \(F(x)=- 3\). This is a horizontal line \(y=-3\) for all \(x\) values greater than or equal to \(2\). At \(x = 2\), since \(x\geq2\) includes \(x = 2\), there is a closed - circle at the point \((2,-3)\) for this part of the piece - wise function.

Answer:

Assuming that option \(B\) has a horizontal line \(y = 3\) with an open - circle at \(x = 2\) and a horizontal line \(y=-3\) with a closed - circle at \(x = 2\), the answer is \(B\).