Question

Find the domain and range of the graph, write as an interval or union of intervals.Find all x-intercepts and y-intercepts.

Answer 1

the domain is the values the function takes on the x-axis and the range it's the same for the y-axis, as we can see this is a rational function, so we need to use the information of the asymptotes to know the values of the domain and range, so:

domain:

the function goes from -infinity to the first asymptote x=-4 and from the same asymptote to infinity

so the domain is:

(-∞,-4) (-4,∞)

range:

go from -infinity to the asymptote on y=2 and from there to infinity, so:

(-∞,2) (2,∞)

and the intercept we can see from the graph:

x-intercept: x=4

y-intercept: y=-2