Question 1031426
your equations are:


y = x


y = (x-3) + 2


to turn y = x into y = (x-3) + 2, you would be shifting the graph of the equation 3 units to the right and then up 2 units.


i made 3 graphs for you.


the first graph is y = x [red line]

the second graph is y = (x-3) [blue line]


the third graph is y = (x-3) + 2 [orange line]


the second graph shows you that you shift the graph of y = x three units to the right by replacing x with (x-3).


the third graph shows you that you shift the grsph of y = (x-3) two units up by adding 2 to the end of the equation.


here's the graphs:


<img src = "http://theo.x10hosting.com/2016/042501.jpg" alt="$$$" </>


<img src = "http://theo.x10hosting.com/2016/042502.jpg" alt="$$$" </>


<img src = "http://theo.x10hosting.com/2016/042503.jpg" alt="$$$" </>


when you correctly converted the equation of y = (x-3) + 2 into y = (x-1), you obscured what was going on.


it's a translation 3 units to the right and then 2 units up.


for example:


when x = 5, .....


the graph of y = x gives you y = 5.


the graph of y = (x-3) + 5 gives you y = 4.


the graph of y = (x-1) gives you y = 4.


the domain of f(x) = (x-3) + 2 is the set of all real values of x.


in interval notation that would be Dx = (minus infinity, plus infinity)


the range of f(x) = (x-3) + 2 is also the set of all real values of x.


in interval notation that would be Ry = (minus infinity, plus infinity).


x can be any positive or negative number.


y can also be any positive or negative number.


here's some references that might help:


<a href = "http://www.mathsisfun.com/sets/domain-range-codomain.html" target = "_blank">http://www.mathsisfun.com/sets/domain-range-codomain.html</a>


<a href = "http://www.mathamazement.com/Lessons/Pre-Calculus/01_Graphs-Functions-and-Models/basics-of-functions.html" target = "_blank">http://www.mathamazement.com/Lessons/Pre-Calculus/01_Graphs-Functions-and-Models/basics-of-functions.html</a>


<a href = "http://www.purplemath.com/modules/fcntrans.htm" target = "_blank">http://www.purplemath.com/modules/fcntrans.htm</a>


<a href = "https://www.mathsisfun.com/sets/function-transformations.html" target = "_blank">https://www.mathsisfun.com/sets/function-transformations.html</a>


<a href = "http://www.purplemath.com/modules/fcns2.htm" target = "_blank">http://www.purplemath.com/modules/fcns2.htm</a>