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3. Function: A relation where every input has exactly one output. Definition Note: A relation is any set of ordered pairs.

4. InputOutput 2 5 1 7 7 4 9 3 This relation is a function because every input has exactly one output. This relation can be represented by the following ordered pairs: ( 2, 4 ) ( 5, 7 ) ( 1, 3 ) ( 7, 9 )

5. InputOutput 2 5 1 7 7 4 9 3 This relation is NOT a function because inputs 1 and 2 each have two outputs. This relation can be represented by the following ordered pairs: ( 2, 4 )( 2, 7 ) ( 5, 7 ) ( 1, 3 )(1, 9 ) ( 7, 9 )

6. When a function is defined by an equation, identify the function by name, f(x), where x identifies the input and f is the name of the function. Note: A function name can be any letter, upper or lower case. Example:f(x) = x + 2 Read as: "f of x..." OR "f as a f unction of x …" Function Notation:

7. 2 5 1 7 7 4 9 3 InputOutput f(x) = x + 2 This represents the function: xf(x) f(2) = 2 + 2 f(5) = 5 + 2 f(1) = 1 + 2 f(7) = 7 + 2 ( 2, 4 ) ( 5, 7 ) ( 1, 3 ) ( 7, 9 )

8. Let’s find a few ordered pairs for the function: f(x) = −2x + 4 (, ) f(0) = -2(0) + 4f(0) = 0 + 4f(0) = 4f(1) = -2(1) + 4f(1) = -2 + 4f(1) = 2f(-1) = -2(-1) + 4f(-1) = 2 + 4f(-1) = 6f(-.5) = -2(-.5) + 4f(-.5) = 1 + 4f(-.5) = 5f(.5) = -2(.5) + 4f(.5) = -1 + 4f(.5) = 3f(2) = -2(2) + 4f(2) = -4 + 4f(2) = 0 04 6 12 -.55.5 3 2 0 Input Output Now, let’s see what happens if we graph these points!

9. (, ) 0 4 6 12 -.5 5.5 3 2 0 Now, let’s see what happens if we graph these points! What happens if we keep graphing points? f(x) = −2x + 4 f(x) x

10. The function, f(x) = −2x + 4, is represented graphically as a line! f(x) x

11. We can use the graph to determine the “output” of the function. Find f (3)  Identify 3 on the x-axis 3  Locate the point on the graph where the x-coordinate is 3  Identify the y-coordinate for that point So, f (3) = − 2 f(x) x

12. Let’s check if this is correct! Remember our function? f(x) = −2x + 4 Find f (3) f(3) = − 2(3) + 4 = − 6 + 4 = − 2 So, f (3) = − 2

13. Find f(4): Using the function definition: f(x) = −2x + 4 f(4) = −2(4) + 4 f(4) = −4

14. Find f(4): Using the graph: f(4) = −4 f(x) x