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U2-S1-L2 Evaluating Functions

U2-S1-L2 Evaluating Functions. Essential Question : How and why do you evaluate functions?. Definitions. 4 Examples of Functions. 3 Examples of Non-Functions. Function Notation. 25. Which do you prefer to write?. Evaluate f when x = 25?. OR. 5.

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U2-S1-L2 Evaluating Functions

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  1. U2-S1-L2 Evaluating Functions Essential Question: How and why do you evaluate functions?

  2. Definitions

  3. 4 Examples of Functions

  4. 3 Examples of Non-Functions

  5. Function Notation 25 Which do you prefer to write? Evaluate f when x = 25? OR 5 The f is the name of the function machine and the value inside the parentheses is the input. The expression to the right of the equal sign shows what the machine does to the input.

  6. Example If f(x) = 2x + 3, find f(5). When evaluating, do not write f(x)! You want x=5 since f(x) was changed to f(5) You wanted to find f(5). So the complete final answer includes f(5) not f(x)

  7. Function Notation – a function that uses f(x) for the output. Example: y = 3x + 2 becomes f(x) = 3x + 2 f(x) is pronounced “f of x” or “f is a function of x” The notation g(x) and h(x) also indicate functions of x Input values are called theindependent variables Output values are called thedependent variables

  8. 1a EXAMPLE Evaluating a function rule Evaluate f(x) = –3x – 10 for x = 6 f(x) = –3x – 10 f(6) = –3(6) – 10 f(6) = –18 – 10 f(6) = –28

  9. 1b EXAMPLE f(a) = –3a + 5 f(a) = –3a + 5 f(a) = –3a + 5 f(-3) = –3(–3) + 5 f(1) = –3(1) + 5 f(4) = –3(4) + 5 f(-3) = 9 + 5 f(1) = –3 + 5 f(6) = –12 + 5 f(6) = 14 f(1) = 2 f(6) = –7 Evaluating a function rule Evaluate the function rule f(a) = –3a + 5 to find the range of the function for the domain {-3, 1, 4}

  10. Check for Understanding How would you explain to another student the process for evaluating expressions? Write your steps in your notes.

  11. Solving v. Evaluating No equal sign Equal sign Solve for x The output is -5. Substitute and Evaluate The input (or x) is 3.

  12. Evaluate Functions from a Graph You can evaluate a function from a table or graph as well by locating the correct input or output value. Find f(0) for each function. Find f(-1) for each function. Find f(x) = 3 for each function.

  13. Function Rule – an equation that describes a function Input Function Rule Domain – is the set of input values Output Range – is the set of output values

  14. 4 16 x = 6 x = 4 x = 2 y = 10 y = 16 y = 22 3x + 4 y = 3x + 4 output input 2 10 6 22

  15. 2 10 4 16 6 22

  16. Application 3 EXAMPLE Suppose your group recorded a CD, now you want to copy and sell it. One company charges $250 plus $3 per CD. The total cost P(c) depends on the number of CDs burned. P(c) = 250 + 3c P(c) 1500 1000 500 200 400 600 Number of CDs

  17. Graphing Functions 4 EXAMPLE Graph the function y = │x│ + 1. Find the domain and range. Domain All real numbers Range {y: y > 1}

  18. Evaluating Functions Evaluating functions helps us find values for solving and graphing. These are solutions to the equation, and points on the graph.

  19. Summary Answer the essential question in detailed, complete sentences. How and why do you evaluate functions? Write 3-5 study questions in the left column to support the notes.

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