graphing a rational function: Quadratic over linear

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graph the rational function: f(x) = 4x^2+6x-6 over 6x+9

draw the asymptotes(if any) and plot at least two points on each piece of the graph

Oct 23rd, 2015

Thank you for the opportunity to help you with your question!

We have the function as

As the function is a rational function therefore

for the vertical asymptote put the denominator=0


x=-3/2 --->vertical asymptote

No horizontal asymptote as the degree of the numerator expression is  not equal to denominator expression.

Oblique asymptote:Divide using long synthetic divison and the quotient of the expression will give the oblique asymptote.

On dividing the oblique asymptote ,y=2x/3  -->oblique asymptote.

The two points lying on the graph are  (0,-2/3) and (3,16/9)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 23rd, 2015

I need two points for each side of the graph making 4

Oct 23rd, 2015


The coordinate of the point lying on the graph are (0,-2/3) and(3,16/9).These point lie on either side of the graph and on it.

Please check and let me know if you have understood and if not I would be glad to help you further.:)


Oct 24th, 2015

i need more points

Oct 24th, 2015

Theres no points for the other side.

Oct 24th, 2015

To find the pair of coordinate substitute the value of x chosen and solve for y.

We have the tables of values as

x              y

0             -2/3

3              16/9

1            4/15

-2             10/3

-3            -10/9

I hope it helps.

Oct 24th, 2015

The point on the other side are the value of x lying to the right graph.

It can be x=3 x=4 x=5 etc

Substitute the value in the expression for y to find the y value.

Oct 24th, 2015

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