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Algebra 1

4.3.3 Comparing Statements in Function Notation

Algebra 14.3.3 Comparing Statements in Function Notation

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Activity

The function W W gives the temperature, in degrees Fahrenheit, of a pot of water on a stove, t t 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 W ( 0 ) = 72 W ( 0 ) = 72

2. What did you and your partner agree is the meaning of W ( 5 ) > W ( 2 ) W ( 5 ) > W ( 2 )

3. What did you and your partner agree is the meaning of W ( 10 ) = 212 W ( 10 ) = 212

4. What did you and your partner agree is the meaning of W ( 12 ) = W ( 10 ) W ( 12 ) = W ( 10 )

5. What did you and your partner agree is the meaning of W ( 15 ) > W ( 30 ) W ( 15 ) > W ( 30 )

6. What did you and your partner agree is the meaning of W ( 0 ) < W ( 30 ) W ( 0 ) < W ( 30 )

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 W W .

Building Character: Creativity

Illustration of a person sitting and thinking, surrounded by creative tools like a pencil, paint swatches, pen, laptop, light bulb, and papers, symbolizing brainstorming or artistic inspiration.

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

The function C gives the temperature, in degrees Fahrenheit, of a pot of coffee x minutes after it is made.

What does the statement C ( 10 ) < C ( 5 ) mean in the context of the problem?

  1. The temperature of coffee after 10 hours was cooler than after 5 hours.
  2. The temperature of the coffee after 10 minutes was warmer than after 5 minutes.
  3. The temperature of the coffee after 10 minutes was cooler than after 5 minutes.
  4. The coffee pot has less coffee in it after 10 minutes than after 5 minutes.

Additional Resources

Comparing Outputs

Function f f gives the depth, in inches, of water in a tub as a function of time, t t , in minutes, since the tub started being drained.

Line graph showing water depth (in inches) over time (in minutes). The depth decreases from 6 to 5 inches at 2 minutes, then drops to below 3 inches at 7 minutes, and stays constant through 10 minutes.

Each point on the graph has the coordinates ( t , f ( t ) ) ( t , f ( t ) ) , where the first value is the input of the function and the second value is the output.

  • f ( 2 ) f ( 2 ) represents the depth of water 2 minutes after the tub started being drained. The graph passes through ( 2 , 5 ) ( 2 , 5 ) , so the depth of water is 5 inches when t = 2 t = 2 . The equation f ( 2 ) = 5 f ( 2 ) = 5 captures this information.
  • f ( 0 ) f ( 0 ) gives the depth of the water when the draining began, at t = 0 t = 0 . The graph shows the depth of water to be 6 inches at that time, so we can write f ( 0 ) = 6 f ( 0 ) = 6 .
  • f ( t ) = 3 f ( t ) = 3 tells us that t t minutes after the tub started draining, the depth of the water is 3 inches. The graph shows that this happens when t t is 6.
  • In the graph, f ( 2 ) > f ( 7 ) f ( 2 ) > f ( 7 ) .
  • f ( 7 ) = f ( 10 ) f ( 7 ) = f ( 10 )
  • f ( 4 ) > f ( 6 ) f ( 4 ) > f ( 6 )
  • f ( 0 ) = 6 f ( 0 ) = 6

Try it

Try It: Comparing Outputs

Function P P gives the depth of the pool water after t t hours of it being refilled.

What does the statement P ( 12 ) < P ( 4 ) P ( 12 ) < P ( 4 ) mean in the context of the situation?

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