First, we will graph y=4x+2 for the domain x<-4. This function has a slope of 4 and a y-intercept of 2. Since the endpoint is not included, we will end the piece with an open circle.
Looking at the graph, we can see that all of the possible y-values are less than -14.
y=2x-6
Next, we will graph y=2x-6 for the domain x≥ -4. This function has a slope of 2 and a y-intercept of -6. Since the endpoint is included, this piece should end with a closed circle.
From the graph, we can see that all y-values that are greater than or equal to -14 will be produced by this portion.
Combining the Pieces
Finally, we can combine the pieces onto one coordinate plane.
Looking at the pieces together, we can see that there are no gaps in the possible values of x. We can also see there are no gaps in the possible values of y. We can use these facts to write the domain and range of the function.
Domain:& All real numbers
Range:& All real numbers
