– ALGEBRA I – Unit 1 – Section 3

Function Notation

Suppose that you have a two-variable relationship…

To generate ordered pairs, you need to choose values for “x” and evaluate…

62 xy

– ALGEBRA I – Unit 1 – Section 3

Function Notation

Here is a table to illustrate some answers:

62 xyX Work Y Ordered Pair4 2(4) + 6 = 8 + 6 = 14 14 (4, 14)9 2(9) + 6 = 18 + 6 = 24 24 (9, 24)0 2(0) + 6 = 0 + 6 = 6 6 (0, 6)3 2(3) + 6 = 6 + 6 = 12 12 (3, 12)

– ALGEBRA I – Unit 1 – Section 3

Function Notation

To change this to function notation, it is just a matter of switching the variable…

62)( xxfLet’s talk about functions notation in a

little more detail…

Function NotationFUNCTION NOTATION –

an alternative way to write an equation that allows you to “name” different equations values that are input into a function

This is read as “f of x”.

62)( xxf

Function Name

Independent Variable

Function NotationWhat is the purpose of writing a relationship in

function notation?

1. Function notation allows you distinguish that a relationship is a function and has the caveat that each member of the domain matches with exactly on value in the range. 2)( xxf

xy Function (or an equation)

Just an equation (not a function)

Function NotationWhat is the purpose of writing a relationship in

function notation?

2. Function notation allows you to give a relationship a “name” and distinguish between different relationships.

2)( xxf xxg 3)( 4)( xxTThis shows that there are three distinct relationships.

2xy xy 3 4xyAre all of the “y’s” referring to same thing?

Function NotationSuppose that you are given a problem like the

following…

).3( Find fThis means that you need to plug 3 in for “x” and simplify. It is just like evaluating an expression.

12666)3(2)3( f

62)( xxf

The ordered pair would be: )12,3(

Function NotationSuppose that you are given a problem like the

following…

).9( Find fThis means that you need to plug 9 in for “x” and simplify. It is just like evaluating an expression.

246186)9(2)9( f

62)( xxf

The ordered pair would be: )24,9(

Function NotationNotice that the process is exactly same as if you were still using “y’s” rather than “f(x)’s”… You

can compare the charts…

X Work Y Ordered Pair4 2(4) + 6 = 8 + 6 = 14 14 (4, 14)9 2(9) + 6 = 18 + 6 = 24 24 (9, 24)0 2(0) + 6 = 0 + 6 = 6 6 (0, 6)3 2(3) + 6 = 6 + 6 = 12 12 (3, 12)

62 xy

Function NotationNotice that the process is exactly same as if you were still using “y’s” rather than “f(x)’s”… You

can compare the charts…

X Work F(x) Ordered Pair4 2(4) + 6 = 8 + 6 = 14 14 (4, 14)9 2(9) + 6 = 18 + 6 = 24 24 (9, 24)0 2(0) + 6 = 0 + 6 = 6 6 (0, 6)3 2(3) + 6 = 6 + 6 = 12 12 (3, 12)

62)( xxf

Try These Problems…

1. f(x) = 5x2 Find f(3).

2. g(y) = 5y2 + 4 Find g(0).

3. h(t) = 2t – 9 Find h(20).

4. T(x) = 3x3 – 4x Find T(2).

**The answers can be found at the end of the PowerPoint.

Evaluate the following functions.

ALGEBRA IS FUN

AND EASY!**Answers: 1) 45 2) 0 3) 31 4) 16