4.2.5 Practice

4.2.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

1. The height of water in a bathtub, $w$, is a function of time, $t$. Let $P$ represent this function. Height is measured in inches and time in minutes.
   
   What does each equation mean in this situation?

1. $P(0)=0$

1. The height of the water is 10 inches after 4 minutes.
2. After 10 minutes, the height of the water is 4 inches.
3. The bathtub starts out with no water.
4. After 20 minutes, the bathtub is empty.

2. $P(4)=10$

1. The height of the water is 10 inches after 4 minutes.
2. After 10 minutes, the height of the water is 4 inches.
3. The bathtub starts out with no water.
4. After 20 minutes, the bathtub is empty.

3. $P(10)=4$

1. The height of the water is 10 inches after 4 minutes.
2. After 10 minutes, the height of the water is 4 inches.
3. The bathtub starts out with no water.
4. After 20 minutes, the bathtub is empty.

4. $P(20)=0$

1. The height of the water is 10 inches after 4 minutes.
2. After 10 minutes, the height of the water is 4 inches.
3. The bathtub starts out with no water.
4. After 20 minutes, the bathtub is empty.

2. Function $C$ takes time for its input and gives a student’s Monday class for its output.
   
   Use function notation to represent: A student has English at 10:00.

1. $C$(10:00)=Monday
2. $C$(Monday)=English at 10:00
3. $C$(10:00)=English
4. $C$(English)=10:00

3. Function $f$ gives the distance of a dog from a post, in feet, as a function of time, in seconds, since its owner left.

1. Find the value of $f(20)$.

1. 3.5
2. 3.4
3. 3.3
4. 3.2
5. 3.1
6. 3.0

2. Find the value of $f(140)$.

1. 3.5
2. 3.4
3. 3.3
4. 3.2
5. 3.1
6. 3.0

4. Looking at the graph below, what does the point $(1980,83)$ mean?

1. There were 83 million more people in 1980 than 1979.
2. In 1980, the world population increased by 83 million people.

5. Function $R$ gives the number of inches of rain after $h$ hours. What does the statement $R(6)=5$ mean?

1. After 6 hours, there was 5 inches of rain.
2. After 5 hours, there was 6 inches of rain.
3. At 6 hours, the rate is 5 inches per hour of rain.

6. Function $R$ gives the number of inches, $T$, of rain after $h$, hours. Choose which function notation represents this situation.

1. $T=R(h)$
2. $h=T(R)$
3. $h=R(T)$
4. $R=T(h)$

7. Use function notation to represent that the number of miles, $m$, a car travels as a function of time, $t$.

1. $t=f(m)$
2. $t=m(f)$
3. $m=f(t)$
4. $f=m(t)$