Objectives

To use function notation

FunctionsA function is a relation in which each

element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).

f(x)x y

Function Notation

Output

InputName of Function

y f x

Given y = 3x – 2 is this a function?To find if an equation is a function:

1)Solve the equation for y.

2)Analyze the equation to determine how many answer it would produce if you substitute a value for x into the equation.So is y = 3x – 2 a function?

We can now replace y with the function notation : f(x) = 3x - 2

Given f(x) = 3x - 2, find:1) f(3)

2) f(-2)

3(3)-23 7

3(-2)-2-2 -8

= 7

= -8

Given h(z) = z2 - 4z + 9, find h(-3)

(-3)2-4(-3)+9-3 30

9 + 12 + 9

h(-3) = 30

Given g(x) = x2 – 2, find g(4)

Answer Now

1. 2

2. 6

3. 14

4. 18

Given f(x) = 2x + 1, find-4[f(3) – f(1)]

Answer Now

1. -40

2. -16

3. -8

4. 4

Given f(x) = 3x - 2, find x if:1) f(x)

3x-2 28

= 28

3x-2=283x=30x=10

f(x) = 28When x = 10

Given h(z) = z2 - 8z - 9, find z if h(z)=0

h(z) = z2 - 8z - 9 0

h(z) = 0When z = 9 or z = -1

h(z) = z2 - 8z – 90= z2 - 8z – 9 0=(z – 9)(z + 1)z = 9 or z = -1

HW

• Pg. 635 # 2, 3, 6, 8 (no sketch)