Question

question
graph the following function on the axes provided.
\\( f(x) = \

$$\begin{cases} -x + 1 & \\text{for} & -6 \\leq x < -2 \\\\ 5 & \\text{for} & x = -2 \\\\ -x + 2 & \\text{for} & -2 < x \\leq 5 \\end{cases}$$

\\)
line closed circle open circle
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Explanation:

Step1: Analyze the first piece

For \( f(x)=-x + 1 \) with \( -6\leq x<-2 \), find two endpoints. When \( x=-6 \), \( f(-6)=-(-6)+1 = 7 \) (closed circle at \((-6,7)\)). When \( x=-2 \), \( f(-2)=-(-2)+1 = 3 \) (open circle at \((-2,3)\)). Draw a line between these points.

Step2: Analyze the second piece

For \( f(x)=5 \) with \( x = -2 \), plot a closed circle at \((-2,5)\).

Step3: Analyze the third piece

For \( f(x)=-x + 2 \) with \( -2

(Note: Since this is a graphing problem, the above steps describe how to plot each part. The actual graphing would be done by following these steps on the provided coordinate system.)

Answer:

To graph the piecewise function:

1. For \( -6\leq x<-2 \): Plot a closed circle at \((-6, 7)\), an open circle at \((-2, 3)\), and draw a line connecting them (using \( y=-x + 1 \)).
2. For \( x=-2 \): Plot a closed circle at \((-2, 5)\).
3. For \( -2

(The graph is constructed by combining these three parts as described.)