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