SOLUTION: Let f(x)= 3x^2+4x+1/3x^2+11x+6 This function has: 1) A y intercept at the point Be sure to put your ordered pair in parentheses. 2) x intercepts at the point(s)

Algebra ->  Equations -> SOLUTION: Let f(x)= 3x^2+4x+1/3x^2+11x+6 This function has: 1) A y intercept at the point Be sure to put your ordered pair in parentheses. 2) x intercepts at the point(s)       Log On


   

Question 1153003: Let f(x)= 3x^2+4x+1/3x^2+11x+6
This function has:
1) A y intercept at the point

Be sure to put your ordered pair in parentheses.
2) x intercepts at the point(s)

Be sure to put your ordered pair in parentheses.
3) Vertical asymptotes at x =

If there is more than one vertical intercept, separate the x-values with a comma.
4) Horizontal asymptote at y =

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29=+%283x%5E2%2B4x%2B1%29%2F%283x%5E2%2B11x%2B6%29............factor
f%28x%29=+%283x%5E2%2B3x%2Bx%2B1%29%2F%283x%5E2%2B9x%2B3x%2B6%29+
f%28x%29=+%28%283x%5E2%2B3x%29%2B%28x%2B1%29%29%2F%28%283x%5E2%2B9x%29%2B%282x%2B6%29%29
f%28x%29=+%283x%28x%2B1%29%2B%28x%2B1%29%29%2F%283x%28x%2B3%29%2B2%28x%2B3%29%29
f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29


This function has:
1) A y intercept at the point: set x=0
f%28x%29=+%28%283%2A0%2B1%29%280%2B1%29%29%2F%28%283%2A0%2B2%29%280%2B3%29%29
f%28x%29=+%281%2A1%29%2F%282%2A3%29
f%28x%29=+1%2F6
y intercept at the point:
(0,1%2F6) ->your ordered pair


2) x intercepts at the point(s) : set f%28x%29=0
+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29=0
+%28%283x%2B1%29%28x%2B1%29%29=0%2A%28%283x%2B2%29%28x%2B3%29%29
+%283x%2B1%29%28x%2B1%29=0
solutions:
if +%283x%2B1%29=0=>3x=-1=>x=-1%2F3
if +%28x%2B1%29=0=>x=-1
x intercepts at the point(s) :
(-1%2F3,0),(-1,0)
3) Vertical asymptotes at x => look for values that make denominator equal to zero
f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29
=> %283x%2B2%29%28x%2B3%29=0,
if %283x%2B2%29=0=>3x=-2=>x=-2%2F3
if %28x%2B3%29=0=>x=-3
solutions: x=-2%2F3, x=-3
MSP11.gif


4) Horizontal asymptote at y =
limit of %283x%5E2+%2B+4x+%2B+1%29%2F%283x%5E2+%2B+11+x+%2B+6%29-%3E1 as x-> ± infinity

MSP11.gif

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