Question

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

$$\begin{cases} 3x & \\text{for} & x < -1 \\\\ x - 4 & \\text{for} & x > 5 \\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.
graph axes with x from -10 to 10 and y from -10 to 10

Explanation:

Step1: Find points for \(y = 3x\) (\(x<-1\))

When \(x=-2\), \(y = 3\times(-2)=-6\).
When \(x=-3\), \(y=3\times(-3)=-9\).
Since \(x < - 1\), we draw a line for \(y = 3x\) with an open - circle at \(x=-1\) (because \(x=-1\) is not included in this part of the domain). The slope of \(y = 3x\) is \(m = 3\).

Step2: Find points for \(y=x - 4\) (\(x>5\))

When \(x = 6\), \(y=6-4 = 2\).
When \(x=7\), \(y=7 - 4=3\).
Since \(x>5\), we draw a line for \(y=x - 4\) with an open - circle at \(x = 5\) (because \(x = 5\) is not included in this part of the domain). The slope of \(y=x - 4\) is \(m = 1\).

Answer:

Graph two lines: one for \(y = 3x\) with \(x<-1\) (using points like \((-2,-6)\), \((-3,-9)\) and an open - circle at \(x=-1\)) and one for \(y=x - 4\) with \(x>5\) (using points like \((6,2)\), \((7,3)\) and an open - circle at \(x = 5\)).