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A translation can move the graph of a function up or down ( Vertical Translation ) and right or left ( Horizontal Translation ).
A vertical translation of function y=f(x) by k units is written in either y-k=f(x) or y=f(x)+k.
If k>0, then the graph moves up.
y=f(x)+4, the graph ends up moving 4 units up.
If k<0, then the graph moves down.
y=f(x)-3, the graph ends up moving 3 units down.
A horizontal translation of function y=f(x) by h units is written y=f(x-h).
If h>0, then the graph moves right.
y=f(x-6), the graph ends up moving 6 units to the right.
If h<0, then the graph moves left.
y=f(x+3), the graph ends up moving 3 units to the left.
Vertical and Horizontal translations can be combines to form y=f(x-h)+k
This causes the graph to move 3 units to the right, and 2 units up.