y= f(x) vs. y= f(x -k)
For y= f(x) goes to y=f(x-k), the graph of f(x) shifts to the right by k if k>0 and shifts to the left by k if k<0. How I remember this is if the equation is (x - k) than you shift the graph to the right because it becomes positive, and if the equation is (x + k ) than you shift the graph to the left because it becomes negative. With Horizontal Translations the graph will only move to the left or right.
example: y= | x | y= | x-3 |
the first graph is the base and the second graph moved to the right 3.
Vertical Translations (y):
y= f(x) vs. y- k = f(x)
For y= f(x) goes to y - k=f(x), the graph of f(x) shifts up by k if k>0 and shifts down by k if k<0. How I remember this is if the equation is y + 3 = f(x) than you shift the graph down because it becomes negative, and if the equation is y - 4 = f(x) than you shift the graph up because it becomes positive. If the equation is y= f(x) +3 it will shift up by 3, and if the equation is y=f(x) -4 the graph will shift down by 4
example: y = x^2 (solid line) and y = x^2 +1(dotted line)
The solid line graph has stayed in its normal position but the dotted line has moved up 1 space.
Both Translations:
When you have both of the translations together you must do both translations. I see it as if a number is grouped with the x like (x - 6) than I know you move the graph to the right by 6. If the equation is y -3 = (x - 6) than I know you have to move the graph up 3 and to the right 6.
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