Question 736854
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(x)=3(x-1)^2/(x^3-8x^2+7x)}}}
{{{r(x)=3(x-1)^2/(x)(x^2-8x+7)}}}
{{{r(x)=3(x-1)^2/(x)(x-7)(x-1)}}}
{{{r(x)=3(x-1)/(x)(x-7)}}}
..
range: (-∞,∞)
..
y-intercept
set x=0
{{{r(x)=3(x-1)/(x)(x-7)=undefined}}}
y-intercept: none
..
x-intercept
set y=0
{{{3(x-1)=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..+....>