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.
h(x)=- 1
First we will graph h(x)=- 1 for the domain x<- 2. This function has a slope of 0, which means it is constant and its graph is a horizontal line. We also know that its y-intercept is - 1. Since the endpoint is not included, this piece should end with an open circle.
Looking at the graph, we can see that all of the possible y-values are equal to - 1.
h(x)=1
Next, we will graph h(x)=1 for the domain x>2. Again, it is a horizontal line. Since the endpoint is not included, we will end the piece with an open circle.
From the graph, we can see that all y-values that are equal to 1 will be produced by this portion.
Combining the Pieces
Finally, we can combine the pieces onto to one coordinate plane.
We can see that there is a gap between the first and second pieces of the function. Our domain will include all possible values of x that are not a part of this gap. Notice that the only possible values of y are - 1 and 1. We can use these facts to write the domain and range of the function.
Domain:& D={x| x<- 2orx>2}
Range:& R={- 1,1}
