SOLUTION: How can I graph this rational function by combining all terms over a common denominator: R(x)=2/3 + 28/3x + 16/x^2

Question 619997: How can I graph this rational function by combining all terms over a common denominator: R(x)=2/3 + 28/3x + 16/x^2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How can I graph this rational function by combining all terms over a common denominator:
R(x)=2/3 + 28/3x + 16/x^2
LCD: 3x^2
R(x)=(2x^2 + 28x + 48)/3x^2
=(2x+4)(x+12)/3x^2
Horizontal asymptote: 2/3 (divide lead coefficient of numerator by lead coefficient of denominator.
Vertical asymptote: set denominator=0, then solve for x.
3x^2=0
x=0 (vertical asymptote)
..
x-intercepts: set y=0, then solve for x
(2x+4)(x+12)=0
2x+4=0
2x=-4
x=-2
and
x+12=0
x=-12
x-intercepts at -2 and -12
..
y-intercept: set x=0, then solve for y
y=48/0= undefined
y-intercept: none
..
number line:
<...+....-12...-....-2....+.....0.....+......>
see graph below as a visual check

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