Need help with a math problem

[zylander]

I have two functions;

f(x)=(2x^3+x^2-13x+6)/(x^3-3x^2-4x+12)

g(x)=(2x^2+5x-3)/(x^2-x-6)

The first can be written out in factored form as: f(x)=2(x-2)(x-.5)(x+3)/(x-2)(x-3)(x+2)

The second can be written out as: g(x)=(x-.5)(x+3)/(x-3)(x+2)

g(x) is basically f(x) with 2 factord out, or you can use synthetic division and "divide" 2 out.

Here is the problem; I have g(x) graphed and now I have to graph f(x) using my graph of g(x). I know its something stupidly easy and I just have to use my remaining factor to transform the graph but I just have no idea how to do it. Can anyone help me out with this? Thanks.

 

[Suspicious-Teach8788]

THere's a factor of 2/(x-2) ?? So you know you have an asymptote? And a stretch factor of 2 in the y-direction?

Not sure.

I don't remember all teh tricks of graphing w/o a calculator. Those days are over for me...

 

[Syringer]

I only graduated as a math major 6 months ago and I have no idea what that means 🙁

 

[esun]

Take g(x) and stretch it by a factor of two along the y-axis (i.e. take every point on your graph and move it farther away from the x-axis by a factor of two) and that gives you f(x).

 

[BrownTown]

Well first off Syringer, I REALLY hope you are kidding about having a math major and not knowing how to multiply by 2. This is Algebra I, not abstract algebra.

So, do what esun said and multiply each point by 2, in otherwords "stretch" the graph out to twice as far from the line y=0. Like you said its trivially simple to do.

 

[zylander]

So I multiply every one of my points by 2 or just the y points of every cordinate?

 

[BrownTown]

just the Y coordinates...

 

[hypn0tik]

In f(x), there is an asymptote at x=2. However, the function approaches a finite value (take the limit). The factor of 2 means that you multiply the y-coordinate of every point by 2.

Edit: Take the limit as x->2 from both sides to see if there is a discontinuity.

 

[zylander]

Great, everything looks like it came out right. Thanks a lot guys, really helped me out.