1.7 - Functions

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y

-6

-4 9

-1 -6

1 1

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y

-6

-4 9 Y

-1 -6 E

1 1 S

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y b.

-6

-4 9 Y

-1 -6 E

1 1 S

x y

-3 6

2 5

3 1

2 4

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y b.

-6

-4 9 Y

-1 -6 E

1 1 S

x y

-3 6

2 5

3 1

2 4

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y b.

-6

-4 9 Y

-1 -6 E

1 1 S

x y

-3 6

2 5

3 1

2 4

1.7 - Functions• A function is a relation in which each

element of the domain is paired with exactly one element of the range.

There cannot be an x-value repeated!

Ex.1 Determine if each is a function.

a. X Y b.

-6 NOT A

-4 9 Y FUNC.

-1 -6 E

1 1 S

x y

-3 6

2 5

3 1

2 4

Ex. 2 If f(x) = x2 – 5, find the following:

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5

f(-9)

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5

f(-9)

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) =

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 =

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 = [(4)2 – 5]

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 =[(4)2 – 5]

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 =[(4)2 – 5] + 2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2

= [16 – 5] + 2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2

= [16 – 5] + 2 = 11 + 2

Ex. 2 If f(x) = x2 – 5, find the following:

a. f(-9)

f(x) = x2 – 5 f(-9) = (-9)2 – 5

= 81 – 5

f(-9) = 76

b. f(6z)

f(x) = x2 – 5

f(6z) = (6z)2 – 5

= 62·z2 – 5

f(6z) = 36z2 – 5

c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2

= [16 – 5] + 2 = 11 + 2

f(4) + 2 = 13

Ex. 2 If f(x) = x2 – 5, find the following: