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)=-2x
First we will graph f(x)=-2x for the domain x≤-2. This function has a slope of -2 and a y-intercept of 0. Since the endpoint is included, this piece should end with a closed circle.
f(x)=x+1
Next, we will graph f(x)=x+1 for the domain 0< x≤6. This function has a slope of 1 and a y-intercept of 1. Notice that the left endpoint is not included so we will begin this piece with an open circle. However, the right endpoint is included and we will end this piece with a closed circle.
f(x)=x-5
Next, we will graph f(x)=x-5 for the domain x>6. This function has a slope of 1 and a y-intercept of -5. Since the endpoint is not included, we will begin this piece with an open circle.
