To graph the given piecewise function, we should think about the graph of each individual piece of the function. Then we can combine the graphs on one coordinate plane.
f(x)=x+3
First we will graph f(x)=x+3 for the domain x<-2. This function has a slope of 1 and a y-intercept of 3. Since the endpoint is not included, this piece should end with an open circle.
f(x)=2x
Next, we will graph f(x)=2x for the domain -2≤ x≤2. This function has a slope of 2 and a y-intercept of 0. Since the endpoints are included, we will begin and end this piece with closed circles.
f(x)=-3x
Next, we will graph f(x)=-3x for the domain x>2. This function has a slope of -3 and a y-intercept of 0. Since the endpoint is not included, we will begin this piece with an open circle.
Combining the Pieces
Finally, we can combine the pieces onto to one coordinate plane.
