1

A function may be specified by a rule or an equation.

Notation:(1) y = x2 + 1 y equals x squared plus one

(2) {(x, y) y = x2 + 1} set of all points (x, y) such thaty = x2 + 1

(3) f(x) = x2 + 1 f of x equals x squared plus one

(4) f: f(x) = x2 + 1 function f maps x to x2 + 1

(5) x x2 + 1 x gets mapped to x2 + 1 throughfunction f

f

Day 2:   Fnct notation, evaluating fnct,  finding domain from equation

NOTATION

2

EVALUATING FUNCTIONSEvaluation = Substitution

A: Evaluate x2 + 3x ­ 1 when x = ­ 2

B: If   f (x) = x2 + 3x ­ 1,evaluate f(­2)

3

   

Find...

a. f (  0  )   =

b. f (  1  )  =

c. f (  ­2  )  =

1:  Let   f (x) = | 2 x  + 1 |  ­   x

0

1

­2

4

Sometimes a function is represented by a graph...

3: Given the graph of f(x)

Find

a.   f (­3) =

b. f (4) = 

c. f (x) = 3

y

x

5

4:

5:

6:

6

DOMAIN FROM EQUATION

Linear

Absolute Value

Quadratic

*Radical

*Fractional

Equation Rule Example

f﴾x﴿ = mx + bf﴾x﴿ = ­ 2x + 3

f﴾x﴿ = a|x ­h| + k

f﴾x﴿ = |x ­ 2| + 5

f﴾x﴿ = ax2 + bx + c

f﴾x﴿ = a﴾x ­ h﴿2 + k

f﴾x﴿ = 3﴾x + 2﴿2 ­ 4

f﴾x﴿ = √stuff

f(x) =     1stuff

f﴾x﴿ = √x ­ 4

f(x) =     1x  ­ 5

f(x) =         12x2 + 5x ­ 3