A level maths: functions & graphs

Modulus function

- when f(x) > 0, modulus = f(x)
- when f(x) < 0, modulus = -f(x)

Modulus graphs

- sketch non modulus graph
- reflect any section below the x-axis in the x-axis

Mapping

- a function if every input has a distinct output
- one to one, many to one
- one to many FUNCTION DOES NOT EXIST as it won’t have a distinct output

Composite functions

- function of a function
- apply inner first, then outer

Inverse functions

- performs the opposite operation
- within the same domain
- only exist as one to one functions
- f(x) & f^-1(x) are inverses of each other
- range of f(x) = domain of f-1(x)
- range of f^-1(x) = domain of f(x)

Modulus graphs of functions

- if the modulus is of the entire function, reflect only that below the x-axis
- if the modulus if only of x within the function, sketch all values for x>0, reflect sketch in the y-axis

Combining transformations

- f(x+a) = horizontal of -a
- f(x) +a = vertical of a
- f(ax) = horizontal stretch of 1/a
- af(x) = vertical stretch of a
- f(-x) = reflection in y-axis
- -f(x) = reflection in x-axis