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1.6 & 1.7: Functions Notes Algebra 1 Name ____________________ Date ____________ Block ___ A function is a relationship between numbers. It’s usually written as an equation and consists of: a set of INPUTS (we call this set the _____________________) and a set of OUTPUTS (we call this set the ___________________) A function pairs each input (x) with EXACTLY one output (y)! Domain = Input = Independent Variable = x-values Range = Output = Dependent Variable = y-values We can display a function in three ways: 1. _______________ Input (x) 0 Output (y) 1 1 2 2 2 4 1 2. __________________ 1 0 2 1 3 4 2 3. ________________ How to Identify a Function Remember: a function is a relationship between input and output values where each input is paired with exactly one output. The easiest way to determine a function: X cannot repeat! (y can) Functions - each x is paired with exactly one y (x doesn’t repeat) x Y 1 3 0 2 -1 1 -2 0 0 1 2 {(2, 4), (3, 5), (4, 6)} 1 3 4 2 NOT FUNCTIONS x Y 6 3 3 1 0 2 3 4 6 4 3 12 {(3, 5), (4, 7), (4, 8)} 2 18 3 is paired with two outputs 1 12 is paired with two outputs 4 is paired with two outputs Tell whether the pairing is a function. 1. 2. 3. x y 5 2 2 6 5 2 4 4 7 5 3 6 3 8 5 4 8 x y 3 x y 8 5 6 3 9 12 __________ __________ __________ The Vertical Line Test The Vertical Line Test is a quick way to help you determine if a relation is a function. If all possible vertical lines cross the graph once or not at all, then the graph represents a function. The graph does not represent a function if you can draw even one vertical line that crosses the graph two or more times. PRACTICE Study each relation and tell whether it is a function or not. Circle Yes or NO. Tell why. 1. YES or NO ______________ 2. YES or NO _____ 3. YES or NO _____ 4. YES or NO ________ 5. {(3, 1), (5, 2), (7, 3)} YES or NO _____ _____ 6. {(2, 1), (3, 1), (4, 2), (5, 2)} YES or NO _____ 7. YES or NO 8. YES or NO Making a Table for a Function To make a table for a function, simply plug in each value of the domain (x) into the function to get the range (y values). Ex. 1 y=x+1 domain: 1, 2, 3, 4 Ex. 2 y = 2x domain: 0, 1, 3, 4 Representing Functions as a Graph We can represent a function as a graph. Simply make an x-y table. Each corresponding pair of input and output values forms an ordered pair we can plot. y=x+1 y = 2x 20.