Analyze each one in the following way: find the domain and range, x and y intercept(s), horizontal asymptote(s), and vertical asymptote(s):
f(x) = 2 / x^2 - 2x - 3
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2 / (x^2 - 2x - 3)
Range is all y values that work. domain is all x values that work.
Here is a graph of it
we can see all y values are in the range except for 0. Which is also the horizontal asymptote.
As for domain those are all the x values that are defined and work for the function
You can interpret this as no division by 0. SO take the denominator portion of the function and set it to 0
(x^2 - 2x - 3)=0
-1, 3 are you answers when you solve for it.
So DOmain is all real numbers excep -1 and 3. ALso it is your V asimptotes
Range is all rea numbers except 0. Also it is H asympote.
That takes care of domain and range and your asymptotes :D
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As for x intercepts
you set f(x)=0 and solve. In other words
2 / (x^2 - 2x - 3)=0
THis is a little harder try it first then let me know if you need help
as for y intercept you go
f(0) in other words plug in 0 to every x in f(x) as so
2 / (0^2 - 2*0 - 3)=y