Functions

Function Transformations

Move, stretch and reflect curves by changing their equations.

Functions overviewDomain and rangeModulus functions

Transformation summary

Vertical translation\[y=f(x)+d\]
Horizontal translation\[y=f(x-c)\]
Vertical stretch\[y=af(x)\]
Horizontal stretch\[y=f(bx)\]
Reflect in x-axis\[y=-f(x)\]
Reflect in y-axis\[y=f(-x)\]
y=f(x)transformed curve
Vertical transformations affect outputs. Horizontal transformations affect inputs and often feel reversed.

Worked example

If \(f(x)=x^2\), describe \(g(x)=(x-3)^2+2\).

The graph of \(g\) is the graph of \(f\) translated 3 units right and 2 units up.