Functional Relationships Worksheets Grade 8

1. 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?
2. Emma is analyzing how the height of a plant changes over time. She records the plant's height each week and notices that the relationship between time (in weeks) and height (in centimeters) can be modeled by the equation y = 2x + 5, where x is the number of weeks and y is the height in centimeters. If Emma wants to predict when the plant will reach a height of 25 centimeters, which equation should she solve?
3. (2.5 × 10³) × (4.0 × 10⁻²) = ?

…and 2 more problems

1. 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.
2. Emma is tracking the height of a plant over 10 days. On day 0, the plant is 5 cm tall. It grows at a constant rate of 2 cm per day for the first 5 days. Then, from day 5 to day 10, it grows at a constant rate of 1 cm per day. Describe qualitatively how the height of the plant changes over the 10-day period, including where it is increasing, decreasing, or constant.
3. Emma is tracking the height of a plant over 8 weeks. The height in centimeters is given by the function h(w) = 3w + 5, where w is the number of weeks since planting. Describe how the height changes as w increases from 0 to 8.

…and 4 more problems

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A second triangle is created by rotating the first triangle 90 degrees counterclockwise about the origin. What are the coordinates of the vertex that was originally at (6,8) after this rotation?
2. Liam is filling a large cylindrical fish tank with water. He starts with the tank empty and turns on a hose that fills the tank at a constant rate of 3 gallons per minute. After 7 minutes, he notices the tank is 21 gallons full. He then turns off the hose and lets the fish tank sit for 5 minutes. During this time, no water is added or removed. After the 5-minute rest, Liam turns the hose back on at the same rate of 3 gallons per minute for another 11 minutes. Describe qualitatively how the volume of water in the tank changes over the entire 23-minute period. In your description, identify each interval where the volume is increasing, decreasing, or constant, and explain what is happening in each interval.
3. Sophia is training for a charity walkathon. She records the distance she walks each day over a two-week period. During the first week (days 1 through 7), she walks 2 miles every day. In the second week (days 8 through 14), she increases her distance by 0.5 miles each day, starting at 2.5 miles on day 8 and ending at 5.5 miles on day 14. After day 14, she feels tired and walks only 3 miles each day for the next three days (days 15, 16, and 17). Describe how the distance Sophia walks each day changes over the 17 days. In your description, identify the intervals where the distance is increasing, decreasing, or constant.

…and 3 more problems