E1
175, 0  x  6

f ( x)   25 x  675
, 6  x  10

3

E3

50, 0  x  4

f ( x)  25 x  50, 4  x  7
 25 x  550

, 7  x  10
3

E5

0, 0  x  4

f ( x)  25 x  100, 4  x  6
 25 x  350

, 6  x  10

4
E7
100
 3 x, 0  x  3

 25 x  125, 3  x  6
f ( x)  
 3
50 x  225, 6  x  8
175, 8  x  10

E9

25 x, 0  x  4

f ( x)  100, 4  x  7
 25 x  475

, 7  x  10
3

E2
0, 0  x  5
f ( x)  
35 x  175, 5  x  10
E4
25 x, 0  x  3

f ( x)  75, 3  x  7
25 x  100, 7  x  10

E6
 25
 3 x  175, 0  x  3

150, 3  x  5
f ( x)  
25 x  25, 5  x  6
 25 x  675
, 6  x  10

3

E8
 25
x  175, 0  x  6

f ( x)   3

125, 6  x  10
E 10
25 x, 0  x  7
f ( x)  
175, 7  x  10
D1
Tom waited four minutes before starting to fill
the bathtub, but after two minutes of adding
water he decided to drain the tub.
D2
After seven minutes of adding water, Terry
noticed the bathtub was full and turned off the
water.
D3
The bathtub was already full so Lynn used the
first six minutes to take a bath and then drained
the water.
D4
Maria thought there was too much water in the
bathtub so she drained some out for the first six
minutes.
D5
After four minutes passed Juan added more water
to the bathtub. He then drained some out after
three more minutes.
D6
D7
Matt added water to the bathtub then drained
some out. He then decided to add some more
water and finally had it the way he wanted for the
last two minutes.
D8
Cindy added water for the first four minutes and
then drained some out during the last three
minutes.
D9
Elise was interrupted before her bath so she did
not start adding water until five minutes had
passed.
D10
Steve drained some water from the bathtub then
turned the water off for two minutes. He then
added some more water and then he let the
bathtub drain for the rest of the time.
D1
Tom waited for minutes before starting to fill the
bathtub, but after two minutes he decided to drain
the tub.
D2
After seven minutes of adding water, Terry
noticed the bathtub was full and turned off the
water.
D3
The bathtub was already full so Lynn used the
first six minutes to take a bath and then drained
the water.
D4
Maria thought there was too much water in the
bathtub so she drained some out for six minutes.
D5
After four minutes passed Juan added more water
to the bathtub. He then drained some out after
three more minutes.
D6
Denise, added water to the bathtub for the first
three minutes, stopped the water while she
answered the phone, and then added more water
during the last three minutes.
D7
Matt added water to the bathtub then drained
some out. He then decided to add some more
water and finally had it the way he wanted for the
last two minutes.
D8
Cindy added water for the first four minutes and
then drained some out during the last three
minutes.
D9
Elise was interrupted before her bath so she did
not start adding water until five minutes had
passed.
D10
Steve drained some water from the bathtub then
turned the water off for two minutes. He then
added some more water and then he let the
bathtub drain for the rest of the time.
Denise added water to the bathtub for the first
three minutes, stopped the water while she
answered the phone, and then added more water
during the last three minutes.
T1
x
f(x)
T3
x
f(x)
0
0
1 2 3
4
5
6
7 10
25 50 75 100 100 100 100 75
T2
x
0
1
2
3
4
5
6
9
f(x) 175 175 175 175 175 175 175 150
T4
0
0
1 2 3
4
5
6
7
10
25 50 75 100 125 150 175 175
T5
x
f(x)
T7
x
f(x)
0
0
1
0
2
0
3
0
4
0
5
25
6
50
10
25
T8
x
f(x)
0
0
3
6
8
9
10
100 75 175 175 175
T9
x
f(x)
T3
x
f(x)
1 2 3 4 5 7
8
9
25 50 75 75 75 75 100 125
T6
x
0
3
4
5
6
9
f(x) 175 150 150 150 175 150
T1
x
f(x)
0
0
0
0
0
0
1
0
2
0
3
0
4
0
5
0
10
175
1 2 3
4
5
6
7 10
25 50 75 100 100 100 100 75
x
0
3
6
7
8
9
10
f(x) 175 150 125 125 125 125 125
T10
x
0 1 2 3 4 5
6
7
10
f(x) 50 50 50 50 50 75 100 125 100
T2
x
0
1
2
3
4
5
6
9
f(x) 175 175 175 175 175 175 175 150
T4
0
0
1 2 3
4
5
6
7
10
25 50 75 100 125 150 175 175
T5
x
f(x)
0
0
1 2 3 4 5 7
8
9
25 50 75 75 75 75 100 125
T6
x
0
3
4
5
6
9
f(x) 175 150 150 150 175 150
T7
x
f(x)
0
0
1
0
2
0
3
0
4
0
5
25
6
50
10
25
T8
x
f(x)
0
0
3
6
8
9
10
100 75 175 175 175
T9
x
f(x)
0
0
1
0
2
0
3
0
4
0
5
0
10
175
x
0
3
6
7
8
9
10
f(x) 175 150 125 125 125 125 125
T10
x
0 1 2 3 4 5
6
7
10
f(x) 50 50 50 50 50 75 100 125 100
25
time
G4
G5
25
time
G7
25
time
G8
time
gallons
time
1
G10
25
1
G6
1
time
G9
25
25
1
time
25
1
gallons
1
1
gallons
25
gallons
time
1
gallons
gallons
1
G3
25
gallons
25
G2
gallons
gallons
gallons
G1
time
1
time
Name: __________________________
__________________________
__________________________
__________________________
Four Faces of a Function
Graph, Equation, Table, Description
Over a ten-minute period the depth of water changes in a bathtub. Sometimes the faucet is
turned on and the bathtub fills up. Sometimes the faucet is turned off and at other times the drain
plug is pulled and water drains out. The x-axis represents the time in minutes and the y-axis
represents the amount of water in gallons.
The purpose of this activity is to provide the opportunity for your team to sort and organize the
different faces of the function so that they match up.
Ten different piece wise functions are represented in four ways:




A graph labeled G1 – G10
A piece wise equation labeled E1 – E10
A table labeled T1 – T10
A description labeled D1 – D10
Match each set of four representations by completing the blanks below to form a matching set of
four cards:
Graphs
Equations
Tables
Descriptions
G1
_________
_________
_________
G2
_________
_________
_________
G3
_________
_________
_________
G4
_________
_________
_________
G5
_________
_________
_________
G6
_________
_________
_________
G7
_________
_________
_________
G8
_________
_________
_________
G9
_________
_________
_________
G10
_________
_________
_________