Which statement best describes how the graph of y = f (x - 2) + 3 is a transformation of the graph of the original function f?
-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?
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.
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
Just realized 2 units left and 3 units up isn't a choice, so I'm confused now
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?
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!
No, the correct answer is "is a shift of the graph of f 2 units to the right and 3 units up." Let me explain how to arrive at this answer:
To understand how the graph of y = f(x - 2) + 3 is a transformation of the graph of the original function f, we need to analyze the equation.
The term (x - 2) inside the parentheses represents a shift of the graph horizontally. When we subtract 2 from the variable x, it causes the graph to move 2 units to the right. This means that for every point on the original graph f, the new graph will be shifted 2 units to the right.
The term +3 outside the parentheses represents a shift of the graph vertically. Adding 3 to the function causes the graph to move 3 units up. So, for every point on the original graph f, the new graph will be shifted 3 units up.
Combining both transformations, the graph of y = f(x - 2) + 3 is a shift of the graph of f 2 units to the right and 3 units up.
Therefore, the correct answer is "is a shift of the graph of f 2 units to the right and 3 units up."