SOLUTION: Find the equations of the vertical and horizontal asymptotes for the graph of the rational function whose equation is f(x) = x/x+3.

Algebra ->  Equations -> SOLUTION: Find the equations of the vertical and horizontal asymptotes for the graph of the rational function whose equation is f(x) = x/x+3.      Log On


   

Question 26865: Find the equations of the vertical and horizontal asymptotes for the graph of the rational function whose equation is f(x) = x/x+3.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equations of the vertical and horizontal asymptotes for the graph of the rational function whose equation is f(x) = x/x+3.
LET Y =X/(X+3)..D.R IS ZERO AT X=-3..SO THIS IS A CRITICAL POINT WHERE THE FUNCTION IS NOT DEFINED.
HENCE WE SPLIT THE DOMAIN OF X
1. FROM -INFINITY TO LESSTHAN -3
2. AND GREATER THAN -3 TO +INFINITY
THE GRAPH FOR DOMAIN
1. FROM -INFINITY TO LESSTHAN -3 IS AS FOLLOWS.
+graph%28+500%2C+500%2C+-50%2C1%2C+-1%2C+50%2C+x%2F%28x%2B3%29%2C1%29+
ALGEBRAICALLY , WE FIND THE RANGE OF Y VARIES FROM 1 TO INFINITY.
SO ASYMPTOTES ARE Y=1 AS X TENDS TO MINUS INFINITY
AND Y TENDING TO INFINITY AS X APPROACHES -3
THE GRAPH FOR DOMAIN
2. FROM GREATER THAN -3 TO +INFINITY IS AS FOLLOW
+graph%28+500%2C+500%2C+-4%2C+50%2C+-50%2C+2%2C+x%2F%28x%2B3%29+%2C1%29+
ALGEBRAICALLY , WE FIND THE RANGE OF Y VARIES FROM MINUS INFINITY TO 1.
SO ASYMPTOTES ARE Y=1 AS X TENDS TO INFINITY
AND Y TENDING TO MINUS INFINITY AS X APPROACHES -3