2. Functions and Graphs Flashcards
Sketching a modulus graph
Draw the regular graph and reflect anything below the x-axis in the x-axis
Solving a modulus for x
Sketch the graph, solve using the same and inverted signs of what is in the modulus and use the graph to show which are needed
Mapping
Something which maps one set of values (inputs) to another (outputs)
Domain
The set of possible inputs
Range
The set of possible outputs
Function
A mapping such that every element of the domain is mapped to exactly one element of the range
(no one-to-many and the whole domain is valid)
One-to-one function
Where each output is derived from only one input
Many-to-one function
Where some outputs can come from more than one input
Finding ranges
Sketch and find stationary points in the domain
Range for a discrete domain
Write a list of discrete values
Piecewise functions
Different rules are used for different intervals within the function
Draw using open circles on the limit for and closed circles for <=, >=
What functions can you find an inverse of
One-to-one, a many-to-one inversed would be one-to-many, which isn’t a function
Graph, domain and range of the inverse
Reflection in the line y = x
Domain of f(x) is range of f^-1(x)
Range of f(x) is domain of f^-1(x)
Intersections of f(x) and f^-1(x)
Lie on the line y=x so solve f(x) = x or f^-1(x) = x
Inversing a quadratic
Start by completing the square
