4.3.3 Comparing Statements in Function Notation
4.3.3 • Comparing Statements in Function Notation
Activity
The function gives the temperature, in degrees Fahrenheit, of a pot of water on a stove, minutes after the stove is turned on.
Take turns with your partner to explain the meaning of each statement in this situation. When it’s your partner’s turn, listen carefully to their interpretation. If you disagree, discuss your thinking and work to reach an agreement.
1. What did you and your partner agree is the meaning of
Compare your answer:
Your answer may vary, but here is a sample: The temperature when the stove was turned on was 72 degrees Fahrenheit.
2. What did you and your partner agree is the meaning of
Compare your answer:
Your answer may vary, but here is a sample: The temperature after 5 minutes was warmer than the temperature after 2 minutes.
3. What did you and your partner agree is the meaning of
Compare your answer:
Your answer may vary, but here is a sample: The temperature of the water after 10 minutes was 212 degrees Fahrenheit.
4. What did you and your partner agree is the meaning of
Compare your answer:
Your answer may vary, but here is a sample: The temperature of the water was the same after 10 minutes and after 12 minutes.
5. What did you and your partner agree is the meaning of
Compare your answer:
Your answer may vary, but here is a sample: The temperature after 15 minutes was higher than the temperature after 30 minutes.
6. What did you and your partner agree is the meaning of
Your answer may vary, but here is a sample: The temperature when the stove was turned on was lower than the temperature 30 minutes later.
7. Sketch a possible graph of function W using the informaiton in the previous questions. If all statements in the previous question represent the situation, sketch a possible graph of function .
Compare your answer:
Building Character: Creativity
Creativity is the ability to think of new solutions. When you approach life with a creative attitude, you are more open to new ideas and possibilities, better able to understand others’ perspectives, and more likely to seek out multiple solutions to problems.
Think about your current sense of creativity. Are the following statements true for you?
- I often seek out new experiences and ways of doing things.
- I like to think of different ways to reach my goals.
Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!
Self Check
Additional Resources
Comparing Outputs
Function gives the depth, in inches, of water in a tub as a function of time, , in minutes, since the tub started being drained.
Each point on the graph has the coordinates , where the first value is the input of the function and the second value is the output.
- represents the depth of water 2 minutes after the tub started being drained. The graph passes through , so the depth of water is 5 inches when . The equation captures this information.
- gives the depth of the water when the draining began, at . The graph shows the depth of water to be 6 inches at that time, so we can write .
- tells us that minutes after the tub started draining, the depth of the water is 3 inches. The graph shows that this happens when is 6.
- In the graph, .
Try it
Comparing Outputs
Function gives the depth of the pool water after hours of it being refilled.
What does the statement mean in the context of the situation?
Compare your answer:
The statement reads “ of 12 is less than of 4.” The input is the time in hours, and the output is the depth of the pool. So, the depth of the pool after 12 hours is less than it was after 4 hours.