What is the transformation f(x-t)+s?
Translation by (t,s)
What is the transformation of af(x)?
One way stretch parallel to y axis by factor ‘a’
What is the transformation of f(ax)?
One way stretch parallel to x axis by factor ‘1/a’
What is the transformation of -f(x)?
Reflection in x axis
What is the transformation of f(-x)?
Reflection in y axis
What is the only combined transformation in which order matters?
Stretches in a direction
Translation in the same direction
How do you determine a combined transformation for translation and stretch in the same direction?
Follow reverse BIDMAS and inverse operations
Follow this rule for what ever direction the change is in
ONLY for changes in ‘x’, changes in ‘y’ follow ordinary orders
What is mapping?
Mapping is any rule which associates two sets of items, referred to as input and output
What are domains and ranges?
Domains are the set of possible inputs
Ranges are the set of possible outputs
What are the 4 types of mapping?
One to one
Many to one
One to many
Many to many
What are the 2 types of mapping of which functions occur?
‘One to one’ and ‘Many to one’
What are the two tests to determine the mapping of a function?
Vertical Test
Horizontal Test
What is the vertical line test?
If a vertical line is drawn on the graph, it must only touch the graph once for it to be a function
What is a horizontal line test?
If a horizontal line is drawn and touches the graph once, it would be one to one. If it touches more than once, it would be many to one
What is the notation for sets of numbers?
R is for real numbers
Z is for integers
Q is for rational numbers
N (or Z+) is for positive integers
How do you test for a vertical asymptote?
Set the expression of the denominator to 0
If this is solvable, the ‘x’ values are a vertical asymptote
How do you test for a horizontal asymptote?
If the denominator and numerator both have the same leading variables, you divide the coefficients. The value is the ‘y’ for asymptote
If denominator degree is greater, asymptote at y = 0
If numerator degree is grater by 1, slant asymptote found by algebraic division
How do composite functions work?
fg(3) = f(g(3))
How does squaring a function work?
f2(x) = f(f(x))
What is an inverse function?
An inverse function describes how you get from an output to an input
How is the domain and range related between a function and its inverse?
The domain and range swap from the original to the composite
What functions can you find an inverse for?
One to one functions
How do you find the inverse for a many to one function?
Restrict the domain so that it does not become one to many when the inverse is found
What is a modulus function?
A function which always has a positive output
