##### 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

We have the function as

As the function is a rational function therefore

for the vertical asymptote put the denominator=0

6x+9=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)

Oct 23rd, 2015

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

Oct 23rd, 2015

Hi

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.

Thanks.

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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Oct 23rd, 2015
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Oct 23rd, 2015
Dec 8th, 2016
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