Functions

Changing Functions

You can move functions very easily:

• \(f(x - a)\) is \(f(x)\) moved horizontally \(a\) units

Warning

\(f(x - 3)\) is \(f(x)\) moved \(3\) units to the right

• \(f(x) + q\) is \(f(x)\) moved vertically \(q\) units

This is how to mirror them:

• \(-f(x)\) is \(f(x)\) mirrored on the x-axis
• \(f(-x)\) is \(f(x)\) mirrored on the y-axis

You can of course stretch/compress functions too:

• \(a \cdot f(x)\) is \(f(x)\) stretched by the factor \(a\)
• \(\frac{1}{a} \cdot f(x)\) is \(f(x)\) compressed by the factor \(a\)