SOLUTION: Given: y = f(x) = (x - 2) / x + 3) find the RANGE and DOMAIN and the VERTICAL and HORIZONTAL ASYMPTOTES.

Algebra ->  Functions -> SOLUTION: Given: y = f(x) = (x - 2) / x + 3) find the RANGE and DOMAIN and the VERTICAL and HORIZONTAL ASYMPTOTES.       Log On


   

Question 158035: Given: y = f(x) = (x - 2) / x + 3) find the RANGE and DOMAIN and the VERTICAL and HORIZONTAL ASYMPTOTES.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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Domain



The denominator CANNOT equal zero, so you must make x%3C%3E-3. This means that the domain is: This says that x can be any real number but -3


Note: the domain in interval notation is


Range



Either graph or find the horizontal asymptote to find the range


The range is: This says that y can be any real number but 1 (which is the horizontal asymptote).



Note: the range in interval notation is


Vertical Asymptote



Since x%3C%3E-3, this means that the vertical asymptote is x=-3


Horizontal Asymptote




Since y%3C%3E1, this means that the horizontal asymptote is y=1. To find the horizontal asymptote without graphing, simply divide the leading coefficients to get 1%2F1=1 (this is only possible if the degrees are equal)


Here's a graph to verify our answers: