Download W4D3 Piecewise Day 2 Warm Up 1. Evalute the following piecewise

W4D3 Piecewise Day 2
Warm Up 1. Evalute the following piecewise function for f( 2 ) , f( 0), f(-4)
2. Graph 32 x − 1
3. Graph −2x + 4
Answers f(2) = 2
f(0) = 4
f(-4) = -7
Coninued Lesson 10 Piecewise
EX 1:
Graph

 3 x − 1;
f (x) = 2

− 2x + 4;

x < 0,

x ≥ 0,
(1)
Graph the first line only to the left of the y-axis. Graph the second line only to the right of the y-axis
An open circle belongs on the first line because it is just < 0
A closed circle belongs on the second line because it is ≥ 0
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 1: Warm Up
EX 2:
Graph
(
f (x) =
|x| − 2;
)
x < 1,
− 2x + 4;
x ≥ 1,
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 2: Ex 2
Open circle at (1, -1) closed circle at (1, 2)
(2)
EX 3:
Graph: Draw a dotted line at x=1 and x = -2 to show the boundary between the functions. Graph each function
on the appropriate side of the line.
f (x) =


 − 2;
5x+4
3 ;



x ≤ −2,

−2 ≤ x ≤ 1,
x ≥ 1,
3;
(3)


5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 3: Ex 2
EX 4:
Graph
(
f (x) =
− |x + 1| + 2;
x ≤ 3,
3x − 7;
x > 3,
)
(4)
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 4: Ex 3
EX 5:
Graph:
(
y = x − 2;
y = −x + 5;
)
−2 ≤ x ≤ 1,
x > 1,
(5)
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 5: Ex 4
Classwork
Do one of these on the front and one on the back of your paper. If you remember how to graph the first 2 functions you can do
#1. If not just do the individual practice problems.
1a. You will need to set up the paper to go from -14 to 14 in both the x and y axes.
p(x) =
 2
x + y 2 = 196;





x2 + y 2 = 100;





x = −2;



 x = 2;

y




y





y



y
= x + 3;
= −x + 3;
= x − 3;
= −x − 3;

ARN 



ARN 




1 ≤ y ≤ 10



1 ≤ y ≤ 10
−8 ≤ x ≤ −2




2 ≤ x ≤ 8




−5 ≤ x ≤ 0



0≤x≤5
1b. You will need to set up the paper to go from -10 to 5 in both the x and y axes
s(x) =


1;
−8 ≤ x ≤ 3,








−6 ≤ x ≤ 3
 5x − 9y = 6;



7x − 4y = −26; −6 ≤ x ≤ −2





7x + 4y = −2;
−2 ≤ x ≤ 2








x + 2y = −6;
−8 ≤ x ≤ 2
Graph Piecewise Practice CW
2.
(
f (x) =
3.
(
f (x) =
4.
(
f (x) =
5.
9.
3x − 2;
x≥1
(8)
)
x < −2
− 2x − 3;
x ≥ −2
−2 ≤ x < 1
− x + 2;
(

−3 ≤ x < −1

x = −1


x > −1
x<4
− x + 1;
x≥4

 1 x + 2;
f (x) = 2

− 3x + 3;
(9)
)
x>1
x + 1;
(7)
)
x + 3;


 2x + 5;
− 3;
f (x) =


− 5x;
f (x) =
8.
x<1
x + 3;
6.
7.
− 2x + 3;
(6)
(10)
(11)
)

x < 0

x≥0
(12)
(13)


|x + 3|; −4 ≤ x < 1





x=1
f (x) = 1;


1


x;
x > 1
4
(14)



 3 + x; −3 ≤ x < 0

− 1;
x=0
f (x) =


 2

x ;
x>0
(15)
5
5
4
4
3
3
2
2
1
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
1
2
3
4
5
1
2
3
4
5
Figure 6: 2 and 3
5
5
4
4
3
3
2
2
1
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
Figure 7: 4 and 5
5
5
4
4
3
3
2
2
1
1
−5 −4 −3 −2 −1
−1
1
2 3
4 5 6
7 8 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
1
2
3
4
5
1
2
3
4
5
Figure 8: 6 and 7
5
5
4
4
3
3
2
2
1
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
Figure 9: 8 and9
14
12
10
8
6
4
2
−14−12−10−8−6−4−2
−2
−4
−6
−8
−10
−12
−14
2 4 6 8 10 12 14
Figure 10: #1 peace
4
2
−10
−8
−6
−4
−2
2
4
−2
−4
Figure 11: #1 star
Exit Pass
1. Graph
(
f (x) =
3x − 2;
)
x ≤ 1,
− x + 5;
x > 1,
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 12: Exit Pass
(16)
White Baord Problems Piecewise
1.
2.
3.
4.
5.


 y = −2;
y = x + 1;


y = 3;
(

x ≤ −2,

−2 ≤ x ≤ 1,
x ≥ 1,
)
y = x − 1;
x < 1,
y = −2x + 6;
x≥1


 y = 1;
y = x;


y = −x + 2;

x ≤ −1,

−1 < x ≤ 2


x>2


3

 y = x + 2;

−4 < x ≤ 0
2

 y = − 1 x + 2; −1 ≤ x ≤ 4

2
(
)
y = −3;
−4 < x ≤ −2
y = 2x + 1;
(17)


−2 ≤ x < 2
(18)
(19)
(20)
(21)
Groupwork Piecewise Intro
Provide graph paper - show how to set it up wtih the same scale! ( count each box as .5 so it’s big enough to cut up)
Groupwork Piecewise Intro
In your groups each of you will graph one of the equations listed below.
A. y=-3x-11
B. y= 34 x + 4
C. y=- 41 x + 3
D. y=4x-10
Graph your function over the domain [-5, 5]
Fold/cut your paper so that A. shows [-5, -4], B. shows [-4, -1] C. shows [-1, 3] D shows [3, 5],
Tape your graphs together.
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Figure 13: Piecewise Functions Intro
My old questions - but not sure this is meaningful at this point in the course.
Write a piecewise function for your graph
Now answer the following questions:
1. What is the y value when x = 0 ?
2. What is the y value when x = 5?
3. What is the y value when x = -4?
4. Which function is represented when x = 2?
5. When is the slope positive?
6. When is the slope negative?