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What are piecewi se functio ns? What are piecewi se functio ns? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2. Erase part of the graph. • What is the domain? • What is the NEW equation? ©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9- 12.F.IF.7b

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Page 1: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

What are piecewise functions?

What are piecewise functions?A __________ function

consists of different function rules for

different parts of the domain.

1. Graph f(x) = x2 + 1.

2. Erase part of the graph.

•What is the domain?

•What is the NEW equation?

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 2: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

What do these symbols mean?

_____________ _____________

CharacteristicsCharacteristics

3. What is the domain for the first (left) segment? The Range?

4. What is the domain for the second (middle) segment? The Range?

5. What is the domain for the third (right) segment? The Range?

6. How many equations do you think you would have to use to write rule for the following piecewise function?

7.What is the domain for the first (left) ray? The Range?

8.What is the domain for the second (right) ray? The Range?

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 3: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

Graphing by tables

Graphing by tables

Both of the following notations can be used to describe a piecewise function over the function’s domain:

f(x) = ]6,2[

)2,5[

if

if

5

2xOR f(x) =

62

25

x

x

,5

,2x

x f(x)-5 -301

1.71.92

2.246

11. How many pieces does your graph have? Why?

12. Are the pieces rays or segments? Why?

13. Are all the endpoints solid dots or open dots or some of each? Why?

14. Were all these x values necessary to graph this piecewise function? Could this function have been graphed using less points?

15. Which x values were “critical” to include in order to sketch the graph of this piecewise function?

9. Complete the following table of values for the piecewise function.

10. Graph the ordered pairs from your table to graph the piecewise function

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 4: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

16. Graph this piecewise function by completing a table of values:

f(x) =

17. How many pieces does your graph have? Why?

18. Are the pieces rays or segments? Why?

19. Are all the endpoints filled circles or open circles or some of each? Why?

20. Was it necessary to evaluate both pieces of the function for the x-value 1? Why or why not?

21. Which x values were “critical” to include in order to graph this piecewise function? Explain.

Graphing by tables

Writing equations

of lines

,210

,3

x

x

71

18

x

x

x f(x) x f(x)

Writing an equation of a line

If you have slope and y-intercept:

If you have slope and a point:

If you have 2 points:

1. 2.

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 5: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

Writing equations

Writing equations

22. Write the equations of the lines that contain each segment.

a) Left segment equation b) Middle equation

c) Right equation

23. List the domain of each segment.

a) Left segment equation b) Middle equation

c) Right equation

24. Put the domain together with the equations to write the equation forthe piecewise function.

)(xf

25.Graph the absolute value function.

26.List all transformations compared to the parent function.

27.Write the absolute value function as a piecewise function.

f(x) = - ⎥x + 2 ⎥

xf(x)

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 6: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

Step Functions

Step Functions

A _________ function is a piecewise function that consists of different constant range values for different intervals of the function’s domain.

1

-2-3 -1-1

2

-3

-2

3

1 3

2

Rou

ndin

g-do

wn

func

tion

Gre

ates

t in

tege

r fu

nctio

n

𝑓ሺ𝑥ሻ= ሾ𝑥ሿ 𝑶𝑹 𝑓ሺ𝑥ሻ= ہ𝑥 ۂ

28.Graph the step function.

29.What is the domain?

30.What is the range?

31.Why is the range not all real numbers?

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b

Page 7: What are piecewise functions? A __________ function consists of different function rules for different parts of the domain. 1. Graph f(x) = x 2 + 1. 2

Step Functions

32. Write the equation of the piecewise function that matches the step function graph.

PRACTICE Use the following piecewise functions to answer the following questions:

a)What is the domain? Range?.

b)What are the x-intercepts? y-intercepts?

c)Describe the end behavior.

d)Where are the intervals of increasing? Decreasing? Remaining constant?

e)Find f(2).

ABC

©2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources MCC9-12.F.IF.7b


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