SOLUTION: Graph this rational function. Start by combining all terms over a common denominator.
R(x)=2/3+28/3x+16/x^2
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Rational-functions
-> SOLUTION: Graph this rational function. Start by combining all terms over a common denominator.
R(x)=2/3+28/3x+16/x^2
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You can put this solution on YOUR website! Graph this rational function. Start by combining all terms over a common denominator.
R(x)=2/3+28/3x+16/x^2
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R(x)=2/3+28/3x+16/x^2
LCD: 3x^2
R(x)=(2x^2+28x+48)/3x^2
R(x)=2(x^2+14x+24)/3x^2
2(x+12)(x+2)/3x^2
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y-intercept
Set x=0, then solve for y
When x=0, function becomes undefined
y-intercept: none
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x-intercept
set y=0, then solve for x
2(x^2+14x+24)=0
2(x+12)(x+2)=0
x-intercepts: -12 and -2
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Horizontal Asymptote:
Since degree of numerator=degree of denominator, divide lead coefficient of numerator(2) by lead coefficient of denominator(3)=2/3
Horizontal Asymptote: 2/3
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Vertical Asymptote:
Set denominator=0, then solve for x
3x^2=0
x=0
Vertical Asymptote: x=0
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number line of function:
<...+...-12...-...-2.....+....0......+......>
I don't have the means to draw a detailed graph of the given function, but I have provided all the information you need to draw one. See the graph below as a visual check on the answers.
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