SOLUTION: Need Clarity on this please.Thanks Given r(x)=3(x-1)^2/x^3-8x^2+7x Find the range of r(x),y intercept,x intercept,Vertical Asymptote,Horizontal Asymptote

Algebra ->  Graphs -> SOLUTION: Need Clarity on this please.Thanks Given r(x)=3(x-1)^2/x^3-8x^2+7x Find the range of r(x),y intercept,x intercept,Vertical Asymptote,Horizontal Asymptote      Log On


   

Question 736854: Need Clarity on this please.Thanks
Given r(x)=3(x-1)^2/x^3-8x^2+7x
Find the range of r(x),y intercept,x intercept,Vertical Asymptote,Horizontal Asymptote
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given r(x)=3(x-1)^2/x^3-8x^2+7x
Find the range of r(x),y intercept,x intercept,Vertical Asymptote,Horizontal Asymptote
***
r%28x%29=3%28x-1%29%5E2%2F%28x%5E3-8x%5E2%2B7x%29
r%28x%29=3%28x-1%29%5E2%2F%28x%29%28x%5E2-8x%2B7%29
r%28x%29=3%28x-1%29%5E2%2F%28x%29%28x-7%29%28x-1%29
r%28x%29=3%28x-1%29%2F%28x%29%28x-7%29
..
range: (-∞,∞)
..
y-intercept
set x=0
r%28x%29=3%28x-1%29%2F%28x%29%28x-7%29=undefined
y-intercept: none
..
x-intercept
set y=0
3%28x-1%29=0
x-1=0
x=1
..
horizontal asymptote: y=0 or x-axis (degree of numerator 1 degree less than that of denominator)
..
Vertical asymptote:
set denominator=0, then solve for x
x(x-7)=0
vertical asymptotes at x=0 and x=7
..
number line:
<..-...0..+...1...-...7..+....>