Question

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

Answer 1

@timo86m

Answer 2

you mean
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

https://www.google.com/search?q=2+%2F+(x%5E2+-+2x+-+3)&oq=2+%2F+(x%5E2+-+2x+-+3)&aqs=chrome..69i57j0l3.658j0&sourceid=chrome&ie=UTF-8

we can see all y values are in the range except for 0. Which is also the horizontal asymptote.
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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.

Answer 3

That takes care of domain and range and your asymptotes :D

Answer 4

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
-.66666=y