Unit 1: Functions Flashcards
Variables
Relationships among quantities
Function
A function f is a rule that assigns to each value x in a set D a unique value denoted f(x)
Domain
The set D of the function
Range
The set of all values of f(x) produced as x varies over the domain
Independent Variable
The variable associated with the domain
Dependent Variable
Belongs to the range
Graph
The set of all points (x,y) in the xy-plane that satisfy the equation y = f(x)
Argument
The expression on which the function works
Vertical Line Test
Every vertical line intersects the graph at most once, otherwise the graph is not a function
Relation
A set of points on a graph that does not correspond to a function
Composite Functions
Given two functions f and g, the composite function f • g is defined by (f • g) (x) = f(g(x))
Symmetric With Respect To The Y-Axis
If whenever the point (x,y) is on the graph, the point (-x,y) is also on the graph
Symmetric With Respect To The X-Axis
If whenever the point (x,y) is on the graph, the point (x,-y) is also on the graph
Symmetric With Respect To The Origin
If whenever the point (x,y) is on the graph, the point (-x,-y) is also on the graph
Even Function
Has the property that f(-x) = f(x) for all x in the domain
Odd Function
Has the property that f(-x) = -f(x) for all x in the domain
Polynomials
Have the form f(x) = anx^n + an-1x^n-1 + … + ax + a0, where the coefficients a0, a1,… are real numbers which cannot equal 0 and the nonnegative integer n is the degree of the polynomial. An nth degree polynomial can have as many n real zeros or roots-values of x at which f(x) = 0
Rational Functions
Are ratios of the form f(x) = p(x)/q(x), where p and q are polynomials
Algebraic Functions
Constructed using the operations of algebra
Exponential Functions
Have the form f(x) = b^x, where the base b cannot equal 1 is a positive real number
Logarithmic Functions
Have the form f(x) = logb x, where b > 0 and b cannot equal 1
Natural Logarithmic Function
Have the form f(x) = ln x, which also has the base b = e
Natural Exponential Function
Have the form f(x) = e^x, with base b = e, where e approx equal to 2.71828
Trigonometric Function
Are sin x, cos x, tan x, cot x, sec x, and csc x