What is a function?

It is a relation between a set of inputs and a set of

permissible outputs with the property that each

input is related to exactly one output.

With the function notation y = f(x), each x value

has only one corresponding y value.

The x-values are the inputs, and the y-values

are the outputs.

1

2

3

4

5

4

3

2

Sum of f and g: (f + g)(x) = f(x) + g(x)

Difference of f and g: (f - g)(x) = f(x) - g(x)

Product of f and g: (f . g)(x) = f(x) . g(x)

Quotient of f and g: (f/g)(x) = f(x)/g(x), g(x) not equal to 0

http://mathonweb.com/help_ebook/html/numbers_1.htm

These functions are the ratio of two polynomials. One field of study where they are important is in stability analysis of mechanical and electrical systems (which uses Laplace transforms).

A rational function is a fraction of polynomials. That is,

if p(x) and q(x) are polynomials, thenp(x)

q(x)

A function of the form f(x) = abx

where a = 0 and b>0 ; b = 1 are

real numbers.

Exponential functions are

functions where the variable is

in the exponent.

bx is the inverse function of logb(x)

There are three basic ways to define the trigonometric

functions. Consider a point (x, y) on the terminal side of an

angle θ in standard position. It lies a distance d away from the

origin.

cosine(θ) = cos(θ) = x

d

tangent(θ) = tan(θ) = y

x

d

ycosecant(θ) = csc(θ) =

x

y

secant(θ) = sec(θ) = d

x

cotangent(θ) = cot(θ) =

sine(θ) = sin(θ) = y

d

The six inverse trigonometric functions are arcsine,

arccosine, arctangent, arccosecant, arcsecant, and

arccotangent.