Domain is the set of values of x for which function is defined.
The given function is not defined at x = -1 and x = 3
Range is f(x) values (or y values) you get, when you put these domain x values in function f(x). Since the function has a horizontal Asymptote at y = 0, so, y = 0 is excluded from Range.
Horizontal Asymptote (HA)
To find HA, divide Numerator and denominator of the function with highest degree (power) of x. Then take limit
divide with highest degree, ,
HA is y = 0
Vertical Asymptote (VA)
For VA, Denominator = 0
(x+1)(x-3) = 0
x = -1 and x = 3
The graph is discontinuous at x = -1 and x = 3
For y-intercept, put, x = 0 in equation,
we get, y = -2/3
y-intercept = -2/3, the graph cuts y-axis at -2/3.
For x-intercept, put, y = 0 in equation,
we do not get any answer from this, so there is no, x-intercept. i.e., the graph does not cuts x-axis
Please see attached graph, the green lines show the asymptotes.