Question

graph the following function on the axes provided. $f(x)=\begin{cases}2x + 5& \text{for }x < - 3\\-5x - 4& \text{for }x>0end{cases}$ click and drag to make a line. click on an endpoint of a line to change it. click the line to delete it.

Explanation:

Step1: Analyze the first - part of the piece - wise function

For \(y = 2x + 5\) where \(x<-3\). When \(x=-3\), \(y=2\times(-3)+5=-6 + 5=-1\). We can find another point, say when \(x=-4\), \(y=2\times(-4)+5=-8 + 5=-3\). Draw a line with an open - circle at \(x = - 3\) (since \(x<-3\)) using these points.

Step2: Analyze the second - part of the piece - wise function

For \(y=-5x - 4\) where \(x>0\). When \(x = 1\), \(y=-5\times1-4=-5 - 4=-9\). When \(x = 2\), \(y=-5\times2-4=-10 - 4=-14\). Draw a line with an open - circle at \(x = 0\) (since \(x>0\)) using these points.

Answer:

Graph the line \(y = 2x+5\) for \(x<-3\) (open - circle at \(x=-3\)) and the line \(y=-5x - 4\) for \(x>0\) (open - circle at \(x = 0\)) on the given coordinate axes.