Sketch Function Graphs Worksheets Grade 8

1. Liam fills a cylindrical tank with water at a constant rate for 5 minutes, then stops for 3 minutes, then drains the tank at a constant rate that is twice the filling rate until empty. Sketch a qualitative graph of the water height in the tank versus time.
2. Mason is filling a rectangular swimming pool with water. He turns on the hose and the water level rises steadily for 12 minutes until the pool is half full. He then stops to check the water temperature, so the water level remains constant for 7 minutes. After that, he turns the hose back on, but now the water level rises at a slower, steady rate for 22 minutes until the pool is completely full. Finally, Mason turns off the hose and immediately gets in the pool, causing the water level to drop suddenly by 2 inches as water splashes out. Sketch a qualitative graph showing the water level (in inches) over time (in minutes) for the entire process.
3. Sophia is on a hiking trip. She starts at the trailhead and hikes uphill for 30 minutes at a steady pace. She then rests for 15 minutes at a scenic overlook. After resting, she hikes downhill back to the trailhead, taking 45 minutes because the downhill path is longer but easier. Sketch a qualitative graph of Sophia's distance from the trailhead (vertical axis) versus time (horizontal axis). Describe the shape of your graph and explain what each segment represents.

…and 3 more problems

1. Liam is designing a rectangular garden with a perimeter of 40 meters. The length of the garden is 4 meters more than its width. What are the dimensions of Liam's garden?
2. Emma is filling a rectangular fish tank with water. The water level rises steadily for 5 minutes, then stays constant for 2 minutes while she adjusts the filter, then rises at a slower steady rate for 3 more minutes until the tank is full. Sketch a graph of water depth (in cm) vs. time (in minutes).
3. Noah is filling a swimming pool. The water level rises quickly at first, then slows down as the pool gets deeper, and finally stays constant when the pool is full. Sketch a graph of water depth vs. time.

…and 5 more problems

1. A rectangular prism is drawn with dimensions 8 cm by 5 cm by 3 cm. A diagonal is drawn from the bottom-front-left corner to the top-back-right corner, passing through the interior of the prism. What is the length of this space diagonal? Round your answer to the nearest tenth of a centimeter.
2. Liam is designing a rectangular garden with a length that is 3 meters more than twice its width. The area of the garden needs to be 65 square meters. What are the dimensions of Liam's garden?
3. A rectangular prism is drawn with dimensions: length = 8 cm, width = 5 cm, and height = 3 cm. A diagonal is drawn from the bottom-front-left corner to the top-back-right corner, passing through the interior of the prism. What is the length of this space diagonal? Round your answer to the nearest tenth.

…and 2 more problems