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Question 63415: Please help me to find these points if they exist, and if they don't please let me know. Thanks so much for your help I do appreciate it.
6.f(x) = x – 3/x + 2 6.g(x) = 3x^2/x^2 + x - 6
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x-intercepts
y-intercepts
Vertical asymptotes
Horizontal asymptotes
Domain of the function
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Please help me to find these points if they exist, and if they don't please let me know. Thanks so much for your help I do appreciate it.
6.f(x) = x – 3/x + 2
PLEASE PUT BRACKETS...
THIS COULD MEAN (X)-(3/X)+2 OR (X)-3/(X+2) OR (X-3)/(X+2)
I AM TAKING IT AS F(X) = Y = (X-3)/(X+2)
x-intercepts
WHERE Y =0?
Y=0 AT X=3...HENCE X INTERCEPT =3
y-intercepts
WHERE X=0?
WHEN X=0,Y=-3/2
HENCE Y INTERCEPT = -3/2
Vertical asymptotes
AT WHAT X VALUE Y TENDS TO INFINITY?
AS X TENDS TO -2...Y TENDS TO INFINITY ...
HENCE X = - 2 IS THE VERTICAL ASYMPTOTE.
Horizontal asymptotes
WHAT IS THE LIMIT OF Y AS X TENDS TO INFINITY?
Y =[1-(3/X)]/[[1+(2/X)]...AS X TENDS TO INFINITY ...Y TEND TO 1.
HENCE Y=1 IS THE HORIZONTAL ASYMPTOTE.
Domain of the function
IS THE PERMISSIBLE VALUES OF X WHICH MAKES THE FUNCTION DEFINABLE
AT X=-2 , THE FUNCTION IS NOT DEFINED AS DIVISION BY ZERO IS NOT ADMISSIBLE.
HENCE DOMAIN IS ALL REAL VALUES OF X EXCEPT -2
THAT IS (-INFINITY,-2)U(-2,INFINITY)
6.g(x) = 3x^2/x^2 + x - 6
SAME AS ABOVE..PUT BRACKETS..ASSUMING IT IS
3X^2/(X^2+X-6) IT IS Y=3X^2/(X+3)(X-2)
HOPE YOU CAN CONTINUE A ABOVE NOW.IF STILL IN DIFFICULTY PLEASE COME BACK
x-intercepts
y-intercepts
Vertical asymptotes
Horizontal asymptotes
Domain of the function
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