FunctionsFunctions

A function is a rule that relates two quantities so that each input value corresponds to exactly one output value.

Define-

Make a table of y = x + 1.Make a table of inputs and outputs.

x x + 1 y

–1

0

1

2

–1 + 1

0 + 1

1 + 1

2 + 1

0

1

2

3

The input x = 2 has two outputs, y = 3 and y = 6. The input x = 3 also has more than one output.

The relationship is not a function.

x y

2 3

3 4

3 5

2 6

To determine if a relationship is a function, verify that each input has exactly one output.

Determine if the relationship represents a function.

Each input x has only one output y.

The relationship is a function.

x y

0 0

1 1

2 2

3 3

Determine if the relationship represents a function.

y = x – 1

Each input x has only one output y.

The relationship is a function.

x x – 1 y

0 0 – 1 – 1

1 1 – 1 0

2 2 – 1 1

3 3 – 1 2

Vertical Line Test

When looking at a graph, you can tell if a drawing is a function if it passes the vertical line test. This means you can draw a vertical line and it will only touch the drawing (graphed figure) one time. If it touches the drawing (graphed figure) more than once, it is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test?

The relationship is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test?

The relationship is a function.

x

y

Write an equation for the Function.

•To write an equation you need to ask yourself, “How did x become y?”•What did I do to “1” in order to get “3?”•What did I do to “2” in order to get “5?”

•Try to find a way to explain the rule.•If I multiplied 1 by 2 and then add 1, I get 3.•If I multiplied 2 by 2 and then add 1, I get 5.

•Check to see if your rule works. Then translate that into a math equation.• y = 2x + 1

x 1 2 3 4 5

y 3 5 7 9 11

Write an equation for the Function.

x 1 2 3 4 5

Y -5 -10 -15 -20 -25

•To write an equation you need to ask yourself, “How did x become y?”•What did I do to “1” in order to get “-5?”•What did I do to “2” in order to get “-10?”

•Try to find a way to explain the rule.•If I multiplied 1 by -5, I get -5.•If I multiplied 2 by -5, I get -10.

•Check to see if your rule works. Then translate that into a math equation.• y = -5x