functions (mga Definitions Lng Sha) Flashcards
the set of all x or input values
Domain Input
the collection of well-defined & distinct objects, called ELEMENTS THAT SHARE A COMMON CHARACTERISTICS
Set
the set of all y or output values
Range Output
A rule that relates values from a set of values (domain) to a second set of values (range)
Function
pair of objects taken in a specific order
Ordered Pair
a set of ordered pair
Relation
FUNCTION OR NOT
{ (1,1), (2,4), (3,3), (4,4)}
Function
FUNCTION OR NOT
{ (1,1), (2,1), (3,3), (4,4)}
Function
FUNCTION OR NOT
{ (2,4), (3,5), (3,6), (4,7)}
NOT Function
FUNCTION OR NOT
{ (5,1), (10,2), (5,3), (20,4)}
Function
(x: domain input, y: range output)
Function set
a function defined by different expressions for different intervals of the input
Piecewise Function
a function that is ratio of two polynomials. in other words, it can be expressed as p(x)/q(x), where p(x) and q(x) ≠ 0
Rational Function
a function in which the variables is in the exponent, it has the form of f(x)=a . b^x, where a is a constant and b is the base (a positive real numbers NOT EQUALS TO 1) and the x is the exponent
Exponential Function
the inverse of an exponential function, it has the form of f(x)= a. logb(x)+c, where a & c are the constant, b is the base of the logarithm(a positive real numbers NOT EQUAL TO 1), and x is the argument of the logarithm
Logarithmic Function
a function g is the inverse function of f if the ordered pairs of g are the ordered pairs of the f written in reversed ordered
Inverse Function
a function is one to one if every second elements is paired to only one first element, and only if its one to one
One-To-One Function
- change f(x) to y
- interchange the variables x and y
- solve for y in terms of x
- change y from step 3 to f^(-1) x
Steps in obtaining the inverse of a function f
the SUM of two functions f(x) and g(x) is denoted by (f +g )(x). this sum is defined as (f + g)(x) = f(x) + g(x)
Addition
the DIFFERENCE between the two functions f(x) and g(x) is denoted by (f - g)(x). the difference is defined as (f - g)(x) = f(x) - g(x)
Subtraction
PRODUCT: the product of two functions f(x) and g(x) is denoted by (f . g)(x), this product is defined as (f . g)(x) = f(x) . g(x)
Multiplication
DIVISION: the QUOTIENT of two functions f(x) and g(x) is denoted by (f/g)(x); this quotient is defined as (f/g)(x) = f(x)/g(x)
Division of Function
the composition of two functions f(x) and g(x) is denoted by (f . g)(x). this composition is defined as (f . g)(x)= f(g(x)). we read this as “f composed of g of x” or “g composed of f of x”
Composition Of Function
a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and g(x) is NOT EQUAL TO ZERO
Rational Function
