Question 64826
<blockquote>"If f(x) = 2x, describe the transformation of the curve for g(x) = -2 x-2

I desparetely need help with this thank you"</blockquote>

I assume you mean the <b>line</b> rather than the 'curve,' as both f(x) and g(x) are linear.  For the record, here is a graph of both:<br>

<center><b>F(x)=2x</b>
{{{graph(200,200,-10,10,-10,10,2x)}}}

<b>G(x)=-2x-2</b>
{{{graph(200,200,-10,10,-10,10,-2x-2)}}}</center><br>

What the question is basically asking is 'How does G differ from F?'<br>

To get from F to G, first we make the "2x" <i>negative</i>.  What happens when you make something negative?  They are 'flipped' along the horizontal axis.  Here are some examples:
<center><b>Graph of F(x)=x</b>
{{{graph(200,200,-10,10,-10,10,x)}}}
<b>Graph of F(x)=-x</b>
{{{graph(200,200,-10,10,-10,10,-x)}}}</center>
See how they're flipped along the horizontal (x) axis?  Let's look at another:
<center><b>Graph of F(x)=x/2</b>
{{{graph(200,200,-10,10,-10,10,x/2)}}}
<b>Graph of F(x)=-x/2</b>
{{{graph(200,200,-10,10,-10,10,-x/2)}}}</center><br>

So, the graph of -2x in regard to 2x, is flipped;
<center><b>Graph of F(x)=2x</b>
{{{graph(200,200,-10,10,-10,10,2x)}}}
<b>Graph of F(x)=-2x</b>
{{{graph(200,200,-10,10,-10,10,-2x)}}}</center><br>

But then we <b>subtract two</b>, what does <I>that</i> do to the graph??  Here are some examples to help verify.  Adding or subtracting to a linear equation (an equation in the form of y=mx+b) moves it along the vertical (y) axis:
<center><b>Graph of F(x)=x</b>
{{{graph(200,200,-10,10,-10,10,x)}}}
<b>Graph of F(x)=x+2</b>
{{{graph(200,200,-10,10,-10,10,x+2)}}}<br>
You know, let's have some fun with this.  Following is a graph of the function Y=X+1, y=x+2, y=x+3, etc., and y=x+0, y=x-1, y=x-2, etc.  Just to illustrate the point; these are all on the same graph:  <font color=red>[EDIT: Upon reviewing, I found that many of the lines are white.  They're plotted, but they're white.  They'll look like cutouts of the x and y axes.]</font>  
{{{graph(200,200,-10,10,-10,10,X-10,x-9,x-8,x-7,x-6,x-5,x-4,x-3,x-2,x-1,x,x
+1,x+2,x+3,x+4,x+5,x+6,x+7,x+8,x+9,x+10)}}}
Pretty cool, huh?  You see, adding any amount to x moves it up that amount, and subtracting an amount <i>from</i> x moves it down that amount.  Therefore, <strong>the difference between f(x)=2x and g(x)=2x-2 is that G(x) moves down two.</strong>  Notice I didn't include g(x)=<b>-</b>2x-2.

Well, making it negative flips it along the x axis (horizontally), and subtracting 2 from it moves it down two units.  Thus, the transformation is <b>the line is flipped along the x axis and moved two units down.</b>
Here are the anticipated graphs:
<center><b>F(x)=2x</b>
{{{graph(400,400,-10,10,-10,10,2x)}}}
<b>G(x)=-2x-2</b>
{{{graph(400,400,-10,10,-10,10,-2x-2)}}}</center><br>

You'll notice that G(x) is simply F(x)'s function flipped along the x axis and moved down 2.  It's as simple as that!  Any questions, feel free to ask.