maths master set

relation 

any relationship between inputs and outputs 

function

a relationship where each input has only one output

are domains written as a ranges or inequalities

inequality

are co domains written as ranges or inequalities

range

whats the domain

a list of x values

whats the range 

a list of y values

to be classed as a function, elements must

• each element in domain can map to only one element in the rnage

• each element in the range must have atleast one element in the domain mapped to it

how to test for a function

vertical line test

difference between range/co domain

range - actual outputs mapped from domain

co domain - ANY POSSIBLE outcomes for a function

whats a composite function

when the output of one function is the input of another

injective function

every output in the codomain has only one input of the domain mapped to it

surjective function definition

every element in the co domain must be mapped by atleast one element in the domain

how to test with a line for an injective function

horizontal line test, if it only hits once its injective

how to test for surjective functions with a line 

horizontal line test, the line drawn will hit the function ATLEAST ONCE 

bijective functions 

every element in the codomain is mapped by one element in the domain

both injective and surjective

how do i square a binomial

T₁² + (2)(T₁)(T₂) + T₂²

x³ - y³

(x-y)(x²+xy+y²)

x³ + y³

(x+y)(x²-xy+y²)

how would i identify if a quadratic equation has 1 real root or 2 equal roots

b² - 4ac = 0

how would i identify if a quadratic equation 2 real roots

b² - 4ac > 0

how would i identify if a quadratic equation has no real roots

b² - 4ac < 0