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

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
RELATED QUESTIONS
The graph of L(x)=log_3(x-1)-2 can be obtained from the graph of f (x)____ What does... (answered by josgarithmetic)

EXPLAIN how the graph g is obtained from the graph of f f(x) = |x| ; f(x) = 2|x| +... (answered by ikleyn)

Hi! I just need help with this last question on my homework, it is fill in the blank.... (answered by ikleyn)

explain how the graph g is obtained from the graph of f. f(x) = |x| ; g(x) = 2 |x| +... (answered by Boreal,ikleyn)

The graph of the function L(x) = log5(x − 1) − 2 can be obtained from the... (answered by josgarithmetic)

I nee your help. How can the graph of g(x)=-(x-3)^2+12 be obtained from he graph of... (answered by josgarithmetic)

hi! so I'm almost done with my homework and I'm unsure of how to do this question. the... (answered by Theo,ikleyn)

completely lost and need a slight push in the right direction! f(x)=3(x+1)^2-12 how... (answered by nerdybill)

Describe how the graph of f(x) = 2^x+4 � 3 can be obtained from the basic exponential... (answered by ewatrrr)