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Understanding Functions: Input-Output Relations | Function Notation Explained

Learn about functions, relations, input-output tables, domains, ranges, and how to determine if a relation is a function. Explore function notation, vertical line tests, and examples to understand the concept better.

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Understanding Functions: Input-Output Relations | Function Notation Explained

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  1. Key Terms Relation – Any set of input that has an output Function – Is a relation that every single input has exactly one output Input (x-coordinate) is also called the Domain Output (y-coordinate) is also called the Range

  2. Making an Input-Output Table Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Domain: {1, 2, 3, 4, 5, 6} Range: {1, 3, 6, 10, 15, 21}

  3. Input the number of seconds after the starting gun in a race to get an output of the number of meters the runner has covered. Domain: {1, 4, 7, 8} Range: {5, 20, 35, 40}

  4. , where x is the place holder (also called a variable ) for the input and y is the place holder for the output. Domain: {-3, 0, 7, 8} Range: {-9, -6, 1, 2}

  5. The rule about only one output each time is crucial and must not be violated. Why is this not a function:

  6. How do I know if it's a function? • Look at the input and output table – Each input must have exactly one output. • Look at the Graph – The Vertical Line test = NO vertical line can pass through two or more points on the graph

  7. Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)} Is this relation a function? YES!

  8. Example 2: Reading the ordered pairs:  (2, 3), (2, 4), (3, 3), (4, 3) Is this relation a function? NO!

  9. Example 3: Is this relation a function? YES!

  10. Example 4: Is this relation a function? NO!

  11. Example 5: Example 6: Is this relation a function? Is this relation a function? NO! YES!

  12. Function Notation By naming a function f, you can write it using function notation: f(x) = mx + b • Function notation is a way to name a function. It is pronounced“f of x” . • f(x) is a fancy way of writing “y” in an equation. • f(x)=2x+4 is the same as y=2x+4

  13. Evaluating Functions • f(x) = x2 – 2x + 3 when x = -3 and x = 4 f(-3) = (-3)2 – 2(-3) + 3 = 9 + 6 + 3 = 18 f(4) = (4)2 – 2(4) + 3 = 16 - 8 + 3 = 11

  14. Name the Function f(x) = ???

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