Algebra Honors ( periods 5 & 6)

Functions Defined by Equations 8-7

Tickets to the LCMS  play cost $5 Production expenses are $500. The school’s profit, p, will depend on n, the number of  tickets sold.    

 profit  - $5 ( number of tickets) - $500   or

p =  5n – 500

The equation p = 5n – 500 describes a correspondence between the number of tickets sold and the profit.

The correspondence is a function whose domain is the set of tickets that could be possibly sold

domain D = { 0, 1, 2, 3, ….}

The range is the set of profits that are possible including “ negative profits” or losses if too few tickets are sold.

Range R= {-500, - 495, - 490, -485…}

If we call this profit function P we can use arrow notation and write the rule 

P: nà 5n – 500

which is read 

“ the function P that assigns 5n – 500 to n” 

or “ the function P that pairs n  with  5n – 500.” We could also use function notation: P(n) = 5n – 500 Which is read

“P of n equals 5n – 500” or

 “ the value of P at n is  5n – 500.”

To specify a function completely, you must describe the domain of the function as well as give the rule. The numbers assigned by the rule then form the range of the function.

 Example: 

List the range of

g:xà4 + 3x- x²    If the domain D = { -1, 0, 1, 2}

Create a chart   or an xy table

replace x with each member of D ( the domain) to find the members of the range R

When x = -1 y = 0

When x = 0 , y = 4

when x = 1 , y = 6

when x = 2 , y = 6

R = { 0, 4, 6}

Notice that the function g assigns the number 6 to both 1 and 2. In listing the range of g, however, we only name 6 once.

Members of the range of a function are called values of the function. 

 The values of this example are 0, 4,  and 6.

To indicate that a function g assigns  to 2 the value 6, you write g(2) = 6

which is read “ g of 2 equals 6” or “ the value of g at 2 is 6.”

Note the g(2) is NOT the product of g and 2. It names the number that g assigns to 2.