SOLUTION: the question concerns the graph of the function f(x)=[x-3]+2 1. I need to explain how the graph of f can be obtained from the graph of y=[x] by using appropriate translation

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Question 1031426: the question concerns the graph of the function f(x)=[x-3]+2
1. I need to explain how the graph of f can be obtained from the graph of y=[x] by using appropriate translation
2. what is the image set of the function f, in interval notation?
I've managed to plot the graph and concluded f(x) = -1+x but otherwise I'm completely stumped.
If anyone can help me, I will be very grateful. Would appreciate workings out, so I can understand future questions.
Many Thanks
Karen
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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:

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:

http://www.mathsisfun.com/sets/domain-range-codomain.html

http://www.mathamazement.com/Lessons/Pre-Calculus/01_Graphs-Functions-and-Models/basics-of-functions.html

http://www.purplemath.com/modules/fcntrans.htm

https://www.mathsisfun.com/sets/function-transformations.html

http://www.purplemath.com/modules/fcns2.htm