Writing Piecewise Functions

1. Writing Piecewise Functions Algebra II Chapter 02 A BowerPoint Presentation

2. What are we doing? We want to take the graph of a piecewise function and turn it into something that looks like this…

3. Step 1 – Where does the graph change? This function appears to have two pieces – one is pink and one is green. What is the value of x when the graph changes from pink to green?

4. Step 1 – Where does the graph change? This function changes from pink to green at

5. Step 1 – Where does the graph change? The left piece of this function is pink . It includes everything where

6. Step 1 – Where does the graph change? The right piece of this function is green . It includes everything where

7. Step 2 – Write the “if” parts of the function Now we can write the “if” parts of the function.

8. Step 2 – Write the “if” parts of the function Now we can write the “if” parts of the function.

9. Step 3 – Replace the ??? with mx+b We need to change the ??? in the function with mx + b . Let’s start with the pink piece.

10. Step 3 – Replace the ??? with mx+b What is the slope (m) of the pink piece?

11. Step 3 – Replace the ??? with mx+b What is the slope (m) of the pink piece? m = 2

12. Step 3 – Replace the ??? with mx+b We can put that slope into the pink piece. m = 2

13. Step 3 – Replace the ??? with mx+b What is the y-intercept (b) of the pink piece?

14. Step 3 – Replace the ??? with mx+b What is the y-intercept (b) of the pink piece? b = –5

15. Step 3 – Replace the ??? with mx+b We can put that y-intercept (b) in the pink piece. b = –5

16. Step 3 – Replace the ??? with mx+b The pink piece of the function is done! Let’s switch to the green piece.

17. Step 3 – Replace the ??? with mx+b What is the slope (m) of the green piece?

18. Step 3 – Replace the ??? with mx+b What is the slope (m) of the green piece? m = –1/2

19. Step 3 – Replace the ??? with mx+b We can put that slope into the green piece. m = –1/2

20. Step 3 – Replace the ??? with mx+b What is the y-intercept (b) of the green piece? We will need to extend the green piece to find it!

21. Step 3 – Replace the ??? with mx+b What is the y-intercept (b) of the green piece? Now we can answer the question !

22. Step 3 – Replace the ??? with mx+b What is the y-intercept (b) of the green piece? b = 3/2 (or 1 ½)

23. Step 3 – Replace the ??? with mx+b We can put that y-intercept (b) in the green piece. b = 3/2 (or 1 ½)

24. Step 4 – We’re done! That’s it! We have successfully written the piecewise function for this graph!

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