Every time I try and simplify ( 3(x/2) - 1 ) / ( -2 (x/2) + 3 ) I come up with a different graph.?

Question

I think it's because I am multipling the top and bottom by 2 to get rid of the compound frac. is that right?

Answer 1

That would be a good way to do it.

Original:
y = ( 3(x/2) - 1 ) / ( -2 (x/2) + 3 )

Multiply top and bottom by 2:
y = ( 3x - 2 ) / ( -2x + 6 )

So when x approaches 3, y will approach infinity (from the left) and negative infinity (from the right). This is a vertical asymptote at x = 3.

Now just look at the coefficients of x in the numerator and denominator, that means the horizontal asymptote will be 3 / -2 (e.g. -3/2).

You can see an image of the graph in the second link.

Answer 2

this could be a quadratic equation. Quadratic equations consistently has a U or a inverted U shape. U shape if the the coefficient of the x^2 is effective. Inverted U if the coefficient is damaging. In you case, the coefficient of x^2 is -a million/3, consequently that is an inverted U. complete the sq. to get the vertex: 6+6x-(a million/3)x^2 =-a million/3(x^2-18x-18) =-a million/3[(x-9)^2-18-80 one] =-a million/3(x-9)^2+33 From this you may get (9, 33) with the aid of fact the vertex. the different factors of activity are the x and y-intercepts. to locate the y-intercept, set x=0. This supply you y=6 to locate the x-intercept, set y=0 and clean up 6+6x-a million/3x^2=0 =>x=[-6+/-sqrt(36+8)]/(-2/3)=9+/-3*sq.... those are each and all of the element you may sketch the mandatory graph.

Answer 3

Yes, multiply top and bottom by 2 to give,

(3*x-2) / (6-2*x)

Answer 4

(3x-2)/2(-x+3)=(3x-2)/(-2x+6)

I don't know how you did it, but I don't see any other way to simplify the above expression.

Answer 5

3x/2 - 1
--------------
-x+3


= (3x-2)/(-2x+6)

x=3 vertical asymptote

y=-3/2 horizontal asymptote.

Answer 6

y=(3x/2-1)/(-2x/2+3)
y=(3x-2)/(-2x+6)

Yes, it would be right...