SOLUTION: find the domain and range 1 please show me how you would graph this. --- x+3

Algebra ->  Functions -> SOLUTION: find the domain and range 1 please show me how you would graph this. --- x+3      Log On


   

Question 904331: find the domain and range 1 please show me how you would graph this.
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x+3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=1%2F%28x%2B3%29 does not exist when x%2B3=0<--->x=-3 .
For any other value of x , f%28x%29=1%2F%28x%2B3%29 can be calculated,
so the domain is all the real numbers except -3 .
x=-3 is the equation of the vertical asymptote.
For x%3C-3 , x%2B3%3C0 and f%28x%29=1%2F%28x%2B3%29%3C0 .
For x%3E-3 , x%2B3%3E0 and f%28x%29=1%2F%28x%2B3%29%3E0 .
As x approaches -3 (from either side),
abs%28x%2B3%29 approaches zero, and abs%28f%28x%29%29=abs%281%2F%28x%2B3%29%29=1%2Fabs%28x%2B3%29 grows without bounds.
As abs%28x%29 increases, abs%28f%28x%29%29=abs%281%2F%28x%2B3%29%29=1%2Fabs%28x%2B3%29 approaches zero,
so y=0 is the horizontal asymptote.
f%28x%29=1%2F%28x%2B3%29 can take any value, except zero,
so its range is all the real numbers except zero.