GEN MATH 12 - Terms of function and relation +

1ST SEM MID TERM

Relation

set of ordered pairs of input and output values where the x is the input (associated with domain of the relation) and the y is the output (associated with range of the relation)

Function

It is when every input value must only have 1 output value in a relation

Vertical line test

It is used to test if a graph is a function or not by seeing if it does not intersect more than 1 point

One to one correspondence

each x-value has only one y-value

One to many correspondence

One x-value has 2 or more y-values

Many to one correspondence

2 or more values of x is associated with the same value of y

Many to many correspondence

x-values to multiple y-values

Piecewise function

a function composed of 2 or more expressions for the different parts of the domain

domain of a function

set of all values of the independent variable x that have a corresponding values depending on the value of y (x values)

range of a function

set of all values of y that can be obtained by the possible values of x (y values)

Linear function

function with a degree of 1 and a graph of a line. The domain and range is all real numbers

Quadratic function

function with degree of 2 and a graph of a parabola. The domain of a quadratic function is the set of real numbers greater than the completed square form or vertex (c - (b/2)²)

Rational function

a function that can be expressed as a ratio of 2 polynomials; the domain of a rational function is the set of real numbers except the 0s of its denominator

Intercepts and zeroes of rational functions

intersection of a graph of a rational function to the x and y axes

y-intercept

the value of y if x = 0

x-intercept

the value of x if y = 0

zeroes of rational function

refers to the value of x that would make the function equal to 0: also the same with the x-intercepts of a rational function

rational expressions

a fraction whose numerator and denominator are both polynomials, ^a/_b where b ≠ 0

Rational equation

an equation whose terms are rational expressions

Least common denominator

least common multiple of all the denominators

Solution

also known as roots and these are values that satisfy a given rational expression

Extraneous solution

values that arrived at upon solving a rational equation but do not satisfy the given equation