Which statement best describes how the graph of y = f (x - 2) + 3 is a transformation of the graph of the original function f?

Question

-is a shift of the graph of f 2 units to the left and 3 units down
-is a shift of the graph of f 2 units to the right and 3 units down
-is a shift of the graph of f 3 units to the right and 2 units up
-is a shift of the graph of f 3 units to the left and 2 units up
-is a shift of the graph of f 2 units to the right and 3 units up

Would it be 2 units to the left and 3 units up?

Answer 1

no. 3 to the right

to move in the positive x- and y- directions,
replace x by x-h
and y by y-k
where h and k are positive numbers

Answer 2

Just realized 2 units left and 3 units up isn't a choice, so I'm confused now

Answer 3

So it would be 3 units right 2 units down?
I'm not going to lie I don't completely get it.

Say we had f (x + 29) would that just be 29 units to the right?

Answer 4

I think I understand now.
For the original questions the answer is sifted to the Right 2 units and Up 3 units right?

For the (x+29) it's shifted to the left 29 units

Someone correct me if I'm wrong please!

Answer 5

no, 2 right and 3 up
you change y=f(x) to
y-3 = f(x-2)
since f(x-h) moves h to the right

try drawing the graphs. Let f(x) = 2x and g(x) = 2(x-3)
you will see that g(x) is the graph of f(x) moved to the right by 3
That is, every new x in g(x) must be 3 greater to produce the graph of f(x)

f(x+29) is 29 to the left
because f(x+29) = f(x - (-29))
so it would shift -29 units to the right, or 29 to the left.

google the topic and you will find many more examples and videos.