Lauren N.

asked • 01/04/16

Intercepts and Asymptotes

Find all of the intercepts and asymptotes of the graph of f(x)= 5x+4/x+2. Be sure to label what type what type pf intercept and asymptote each is

2 Answers By Expert Tutors

By:

Michael J. answered • 01/04/16

Tutor
5 (5)

Best Afterschool Tutor to Prepare You For Your Regents

Carmen M. answered • 01/04/16

Tutor
5.0 (33)

Mechanical Engineer, Master in Science

Lauren N.

I am a bit confused when i graph this on my calculator it clearly crosses the x any y axis at y=5 and x=-2, when I set the x's in the equation to zero to solve for the y intercept I get y=2 and x=-4/5 for an x intercept how is there no real solutions if the graph clearly states them and the calculator graph values do as well?
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01/04/16

Carmen M.

Hi Lauren
With the parenthesis f(x)= (5x+4)/(x+2 ) is a totally different function that the one I help you with. This is a rational function.  But the methodology is the same.
To find the y intercept you make x =0, then f(0)=2 
To find the x intercept you make y =f(x)=0, then 5x+4=0, solve for x=-4/5, this is the x intercept. 
To find the vertical asymptote you have to look at the denominator which can not the the value of zero, therefore x=-2 is a vertical asymtote.
To find the horizontal asymptotes compare the order of the denominator and numerator polynomials, since the have the same order ratio of both higher order coefficient represent the asymptote y=5/1, then y=5 is a horizontal asymptote. 
 
The answer the other tutor gave you is the correct one for the equation with the parenthesis.
 
Carmen
 
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01/04/16

Michael J.

If the function was
 
f(x) = 5x + (4 / x) + 2,
 
then Carmen's answer would have been the favorable one.
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01/05/16

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