Algebra and Functions Flashcards
Domain of a function
Set of values that are allowed to be the input
Range of a function
Set of values of all possible outputs
Inverse function method
Change X’s and Y’s
Solve to make Y the subject again
ff^-1(x) =
x
Function and inverse on a graph
reflection in the line y = x
Composite function
Input -> Function 1 -> Output/Input 2 -> Function 2 -> Output 2
Quadratic formula
x = [-b +- sqrt(b^2-4ac) ]/ 2a
Discriminant
b^2 -4ac
Two real roots (discriminant)
b^2 - 4ac > 0
two points touch x axis
One real root
b^2 - 4ac = 0
one point touches x axis
No real roots
b^2 - 4ac < 0
does not touch x axis
Finding turning point
e.g. x^2 + 2x + 2 = 0
Complete the square (x + 1)^2 + 1 = 0
Find minimum value of (x+1) = 0, x = -1
Solve for y coordinate
Solving quadratic inequalities
Factorise and find roots
Draw quadratic on graph
Determine inequality based on > or <
Polynomial definition
Algebraic expression with non-negative integer indices only e.g. x^2, y, 5
How to divide polynomials
Bus stop method (long division) based on highest power term and repeat
If the divisor is a factor r = 0
If not, r =/= 0
Factor Theorem
If f(p) = 0, then (x - p) is a factor of f(x)
If (x - p) is a factor of f(x), then f(p) = 0
Remainder theorem
If (x - p) has a remainder, q, from f(x), f(p) = q
If f(p) = q, (x - p) has a remainder, q, from f(x)
