## Problem 746

For the given function, find each of the following:

a)      Intercept

b)      Vertex

c)       Maximum or minimum

d)      Range

g(x) = (x-1)2 – 4

Solution:-

a)      x – intercept:- 1,3; y – intercept: -3

b)      Vertex (1,-4)

c)       Minimum : -4

d)      y >= -4

## Polynomial Function

Polynomial Function

A polynomial function of degree n is defined by

f(x) = anxn + an-1 xn-1 + ….. +a1x + a0,..

for real numbers an, an-1,…..a1, and a0 , where an ≠ 0 and n is a whole number.

## Use function notation

Use function notation

When a function f is defined with a rule or an equation using x and y for the independent and dependent variables, we say “y is a function of x” to emphasize that y depends on x. We

use the notation

y = f (x),

called function notation, to express this and read f (x) as “f of x.” (In this special notation the parentheses do not indicate multiplication.) The letter f stands for function. For example, if y = 9x – 5, we can name this function f and write

f (x) = 9x –  5.

Note that f (x) is just another name for the dependent variable y. For example, if y = f (x) = 9x – 5 and x = 2, then we find y, or f (2), by replacing x with 2.

y  =  f (2) = 9 . 2 – 5

= 18 – 5

= 13.

For function f, the statement “if x = 2, then y = 13” is represented by the ordered pair (2, 13) and is abbreviated with function notation as

f (2) = 13.

Read f (2) as “f of 2” or “f at 2.” Also,

## Variations of the Definition of Function

Variations of the Definition of Function

a.  A function is a relation in which, for each value of the first component of the ordered pairs, there is exactly one value of the second component.

b.  A function is a set of ordered pairs in which no first component is repeated.

c.  A function is a rule or correspondence that

## Define and identify relations and functions

Define and identify relations and functions

Since we can write related quantities using ordered pairs, a set of ordered pairs such as

{(5, 40), (10, 80), (20, 160), (40, 320)}

is called a relation.

Relation

A relation is any set of ordered pairs.

A special kind of relation, called a function, is very important in mathematics and its applications.

Function

A function is a relation in which, for each value of the first component of the ordered pairs, there is exactly one value of the second component.