Relations and Functions

Virtual Learning Day

​Algebra

What is a relation?

A relation shows a relationship between INPUT and OUTPUT.

What is a relation?

A set of ordered pairs (x,y) is an example of a relation.

​Every function is a relation, but not all relations are functions.

What is a function?

A function is a relation, where each input value (x) has exactly one output value (y).

Multiple Choice

Does this mapping diagram represent a function or not a function?

• A function, there is one output for every one input

• A function, all inputs are and outputs are different

• Not a function, there are two outputs for the input of -3

• Not a function, the input of 2 has an output of 2

Multiple Choice

This is a relation, but NOT a function.

Why not?

• There are different inputs for the one output.

• The one input has multiple outputs.

• There is one output for one input.

• There are multiple ordered pairs.

Multiple Choice

List the ordered pairs represented in the mapping diagram.

• {-1, 0, 3, 4}

• (-3, 3)

  (1, -1)

  (2, 0)

  (-4, 4)

• (-1, 1)

  (0, 2)

  (3, -3)

  (4, -4)

• (-1, 1)

  (0, 2)

  (4, -4)

Multiple Choice

Which of the values can be substituted for x in the table, to make this relation a function?

• 7

• 5

• -1

• -2

Evaluating a Function

Using a Function Rule

Evaluating a Function

Using a Function Rule

​Lets say you have f(x) = 2x + 5, and you are solving for f(3).

f(3) = 2(3) + 5
f(3) = 6 + 5
f(3) = 11

Multiple Choice

• 32

• -8

• -32

• -48

Multiple Choice

• -9

• 9

• -1

• 1

Multiple Choice

• 1

• 2

• 14

• -14

Multiple Choice

• -12

• 12

• 7

• 1