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Functions

Tables and Graphs Chapter 2.4. Functions. In a function…. Choose whichever definition your prefer to copy down:. Each dependent variables relates to exactly one independent variable. With every input there is one output. For every x , there is one (and only one) y. In functions:.

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Functions

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  1. Tables and Graphs Chapter 2.4 Functions

  2. In a function… Choose whichever definition your prefer to copy down: • Each dependent variables relates to exactly one independent variable. • With every input there is one output. • For every x, there is one (and only one) y.

  3. In functions: You can have different inputs with the same output, but you cannot have the same input with two or more outputs. Input Output Input Output NOT a FUNCTION FUNCTION

  4. Think of it like a soda machine: Input Output In a function, you put one value in, and you get something else out.

  5. Think of it like a soda machine: Input Output If you press buttons 1, 2, or 3 you will get the same output (Pepsi) because that is how the machine is designed.

  6. Think of it like a soda machine: However, if you press the same button, and two different sodas came out, you would know the machine was broken. It is not functioning correctly. Input Output

  7. Recognizing Functions in Tables: 1. 2. 3. FUNCTION NOT FUNCTION

  8. Functions in Graphs: If there can only be one output (y) for every input (x) then the graph cannot look like: y Does a graph pass the “vertical line test”? x

  9. Recognizing Functions in Graphs y y 1. 2. x x NOT A FUNCTION FUNCTION

  10. Each function has a domain and range:Domain: All possible inputs (x’s)Range: All possible outputs (y’s)

  11. Find the range when the domain is… • Plug in the different values into the equation. • Put the answers in a set. If the domain is {-2, 1, 6} what is the range? y = 2x + 3 y = 2(-2) + 3 = -4 + 3 = -1 y = 2(1) + 3 = 2 + 3 = 5 y = 2(6) + 3 =12 + 3 = 15 Range: {-1, 5, 15}

  12. Homework: pg 76-77 (9-21 all, 25-35 odds) • Show work when possible, follow directions completely (answer all parts.) • Notebook Check and Basic Skills Quiz • NEXT CLASS!

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