a rule that assigns to each element in set A one and only one element in a set B
The set A - which input values can be input into the rule.
The set B - what output values are possible.
A variable whose value the user sets.
A variable that depends on the chosen independent variable
a set of two numbers where the first is the x value and the second is f(x). (x,f(x))
Graph of a funcion
the set of all points (x,y) in the xy-plane such that x is in the domain of ? and y=f(x)
piecewise defined function
A function that is defined by more than one rule.
Graph of an equation
the set of all ordered pairs (x,y) that satisfy the given equation.
A curve in the xy-plane is the graph of a function y-f(x) if and only if each vertical line intersects it in at most one point
Let f and g be functions. The composition of g and f is the function g o f defined by: (g o f)(x) = g(f(x)) The domain of g o f is the set of all x in the domain of f such that f(x) lies in the domain of g.
a function of the form f(x) = ax^n + bx^n-1 +...+ cx + d. where a-d are constants and a does not equal 0
A polynomial function of degree one. Example: f(x) =2x-5
A polynomial function of degree 2. Example: 2x^2+2x+2
A polynomial function of degree 3
The quotient of two polynomials
functions of the form f(x)=x^r where r is any real number.
p=f(x) where p measures the nit price and x measures the number of units of the commodity in question.
p=f(x) - generally increasing - relates the unit price and the quantity supplied.
When the quantity produced is equal to the quantity demanded.
The quantity produced at market equilibrium
the price at market equilibrium
limit of a function
the function ? has the limit L as x approaches a, if the value f(x) can be made as close to the number L as we please by taking x sufficiently close to (but not equal to) a.
A function where the limit does not exist as x approaches a value
when something results in an answer of 0/0
limit of a function at infinity
The function ? has the limit L as x increases without bound, if ?(x) can be made arbitrarily close to L by taking x large enough.
right-hand limit of a function
the function ? has this kind of limit as x approaches a from the right, if the values f(x) can be made as close to L as we please by taking x sufiiently close to (but not equal to ) a and to the right of a.
left-hand limit of a function
the function ? has this kind of limit as x approaches a from the left, if the values f(x) can be made as close to L as we please by taking x sufiiently close to (but not equal to ) a and to the left of a.
continuity of a function at a point
A function ? is continuous at the point x=a if the following conditions are satisfied. 1. ?(a) is defined. 2. lim as x approaches a of f(x) exists. and 3. lim as x->a f(x)=f(a)
tangent line to the graph of ?
A line that touches the graph of ? only once and has a slope of lim h->0 (f(x+h) - f(x))/h
a function which has a derivative on the interval [a,b]
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