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 < 0 , if 1/2 < x < 3/2

Explanation:

Step1: Find the function for \(-3 \leq x < 0\)

We have two points on this segment: \((-3, -6)\) and \((0, 0)\). The slope \(m\) is calculated as \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-6)}{0 - (-3)}=\frac{6}{3} = 2\). Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((0,0)\), we get \(y=2x\). So for \(-3\leq x < 0\), \(f(x)=2x\).

Step2: Find the function for \(\frac{1}{2}

From the graph, we can see that this is a horizontal line. The \(y\) - value of this line is \(3\) (since the open circle and the horizontal line have \(y = 3\)). So for \(\frac{1}{2}

Answer:

For \(-3\leq x < 0\): \(2x\)
For \(\frac{1}{2}