Functional Relationships Worksheets Grade 8

1. Noah is tracking the height of a bamboo plant over several days. On Day 0, the plant is 10 cm tall. From Day 0 to Day 4, the plant grows at a steady rate of 3 cm per day. From Day 4 to Day 7, the plant grows more slowly, adding only 1 cm per day. After Day 7, the plant stops growing and remains at the same height. Describe qualitatively how the height of the bamboo plant changes over time. In which intervals is the function increasing, and where is it constant?
2. Charlotte is tracking the height of a plant over 8 weeks. The height (in cm) at the end of each week is: Week 1: 4 cm, Week 2: 7 cm, Week 3: 9 cm, Week 4: 10 cm, Week 5: 10 cm, Week 6: 10 cm, Week 7: 13 cm, Week 8: 17 cm. Describe qualitatively how the height changes over time, specifying intervals where the function is increasing, decreasing, or constant.
3. Liam is designing a rectangular garden with a length that is 3 feet more than twice its width. The total area of the garden is 65 square feet. What are the dimensions of Liam's garden?

…and 4 more problems

1. Emma is comparing two job offers for her summer internship. Company A offers a base pay of $200 per week plus $15 for each project completed. Company B offers a base pay of $150 per week plus $20 for each project completed. Emma wants to know how many projects she would need to complete each week for both companies to pay the same total weekly amount. How many projects would that be?
2. (2.4 × 10⁵) ÷ (6 × 10²) = ?
3. A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. If you double all three dimensions to create a larger prism, how many times greater will the volume of the new prism be compared to the original?

…and 3 more problems

1. Mason is observing a hot air balloon ascending and descending over time. He records its height above the ground every 10 minutes. From 0 to 20 minutes, the balloon rises steadily from 0 meters to 40 meters. Then, from 20 to 30 minutes, it stays at a constant height of 40 meters. From 30 to 50 minutes, it descends steadily back to the ground (0 meters). Describe qualitatively how the height of the balloon changes over time in each of these three time intervals: 0–20 minutes, 20–30 minutes, and 30–50 minutes.
2. Describe how the function y = 3x² - 5 changes as x increases from -3 to 0, and then from 0 to 3. Is the function increasing, decreasing, or constant in each interval?
3. Noah is tracking the water level in a large tank as it is being drained for cleaning. The tank starts with 1800 gallons of water. He opens the drain valve, and water flows out at a constant rate of 12 gallons per minute. Describe qualitatively how the amount of water in the tank changes over time from the moment the valve is opened until the tank is empty. Be sure to state whether the relationship is increasing, decreasing, or constant, and explain why.

…and 4 more problems