Question

$$ f ( x ) = left{ \begin{array} { l l l } { - 2 x - 4 } & { \text { for } } & { - 4 leq x < - 1 } \\ { 2 } & { \text { for } } & { - 1 < x < 4 } end{array} ight. $$

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: Plot the first piece of the function

For \(y = - 2x-4\) when \(-4\leq x<-1\).
Find two points:
When \(x=-4\), \(y=-2\times(-4)-4=8 - 4=4\).
When \(x = - 1\), \(y=-2\times(-1)-4=2 - 4=-2\).
Plot the line segment from \((-4,4)\) to \((-1,-2)\) (with an open - circle at \(x=-1\)).

Step2: Plot the second piece of the function

For \(y = 2\) when \(-1Plot a horizontal line \(y = 2\) from \(x=-1\) (open - circle) to \(x = 4\) (open - circle).

Answer:

The graph of the piece - wise function \(f(x)\) is composed of a line segment \(y=-2x - 4\) for \(-4\leq x<-1\) (from \((-4,4)\) to \((-1,-2)\) with an open - circle at \(x=-1\)) and a horizontal line \(y = 2\) for \(-1