Functions Functions

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. xx + 1y – –

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. xy 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. xy

Determine if the relationship represents a function. y = x – 1 Each input x has only one output y. The relationship is a function. xx – 1y 00 – 1– 1 11 – – – 12

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 x12345 y357911

Write an equation for the Function. x12345 Y 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