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Translations of FunctionsGiven the function f(x)f of x:
Transformation Notation | Transformation Description |
---|---|
f(x+k)f of the quantity x plus x | Translates the graph of f(x)f of x left when k is positive and right when k is negative. |
f(x)+kf of x plus k | Translates the graph of f(x)f of x up when k is positive and down when k is negative. |
Given the function f(x)f of x:
Transformation Notation | Transformation Description |
---|---|
-negativef(x)negative f of x | Reflects the graph of f(x)f of x in the x-axis. |
f(-negativex)f of negative x | Reflects the graph of f(x)f of x in the y-axis. |
Given the function f(x)f of x:
Transformation Notation | Transformation Description |
---|---|
kf(x)k times f of x |
Dilates the graph of f(x)f of x when |k|>1the absolute value of k is greater than one. Reduces the graph of f(x)f of x when 0<|k|<1the absolute value of k is between 0 and 1. |
f(kx)f of the quantity k times x |
Reduces the graph of f(x)f of x when |k|>1the absolute value of k is greater than one. Dilates the graph of f(x)f of x when 0<|k|<1the absolute value of k is between 0 and 1. |