Functions Functions. A function is a rule that relates two quantities so that each input value...
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Transcript of Functions Functions. A function is a rule that relates two quantities so that each input value...
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