Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). the graph represents the piecewise function: f(x) = { , if -3 ≤ x < -1 , if -1 ≤ x ≤ 1

Explanation:

Step1: Analyze the first piece ($-3 \leq x < -1$)

The graph from \(x = -3\) (closed dot) to \(x = -1\) (open dot) is a line. Let's find the slope and equation. The points are \((-3, 0)\) and \((-1, 2)\). The slope \(m=\frac{2 - 0}{-1 - (-3)}=\frac{2}{2}=1\). Using point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(-3,0)\), we get \(y-0 = 1\times(x + 3)\), so \(y=x + 3\).

Step2: Analyze the second piece ($-1 \leq x \leq 1$)

The graph from \(x=-1\) (closed dot) to \(x = 1\) (closed dot) is a horizontal line. At \(x=-1\) and \(x = 1\), the \(y\) - value is 5. So the equation is \(y = 5\).

Answer:

For \(-3\leq x<-1\): \(x + 3\)
For \(-1\leq x\leq1\): \(5\)