2 Functions of One Variable Flashcards
When is a function monotonic?
When it is increasing or decreasing over a set domain
When is a function strictly increasing?
When x1
What is the format of a power function
Y=Ax^r
Where r and A are constants
What are examples of economic applications of power functions?
Production function y=x^r (0
What is the format of an exponential function
Y=Ab^x
Where A and b are constants
What is the inverse of y=ln(x)
Y=e^x
X=e^y ??
How are y=ln(x) and y=e^x graphically related?
They are symmetrical in the line y=x
What is a^(loga(x)) equal to?
X
How else can log(xy) be written?
Log(x) + log(y)
How else can log(x) + log(y) be written
Log(xy)
How else can log(x/y) be written?
Log(x)-log(y)
How else can log(x)-log(y) be written
Log(x/y)
How else can log(x^p) be written
Plog(x)
How else can plog(x) be written
Log(x^p)
What is loga(a) equal to?
1
How else can loga(x)/loga(b) be written?
Logb(x)
Describe the graphical change that occurs when t(t) is created by adding f(t) and m(t)
t(t) is the vertical sum of m(t) and f(t)
If F(x)=f(x) x g(x) what is F(x) called?
The product of f and g
If F(x)=f(x)/g(x) what is F(x) called?
The quotient of f and g
What is a composite function?
When two functions are combined to create a composite function
E.g h(x)= f(g(x))
When does an inverse function exist?
If the original function is strictly monotonic. ie the function is one to one
Domain
Set on which a function is defined
Codomain
Set on which output of f(x) is constrained to fall
Range
Set of elements of Y associated with elements of X
What is a continuous function?
One which can be drawn without lifting the pen from the paper ie no jumps
