Domain and Range Worksheets Grade 9

1. Matiu is designing a water fountain for a park. The height of the water stream above the fountain basin is modeled by the function h(x) = -0.25x² + 4x, where h is the height in feet and x is the horizontal distance in feet from the nozzle. The fountain's basin extends 16 feet horizontally from the nozzle. The park requires that the water must be at least 6 feet high for visual effect. Graph the function and determine the domain and range of h(x) for this fountain design, considering the basin's edge and the requirement that height cannot be negative.
2. f(x) = 4x² - 7x + 5; f(2) = ?
3. Maya is designing a skateboard ramp with a parabolic shape. The height of the ramp above the ground is modeled by the function h(x) = -0.5x² + 4x, where h is the height in feet and x is the horizontal distance in feet from the starting point. What is the maximum height the ramp reaches, and at what horizontal distance does this occur?

…and 4 more problems

1. f(x) = 2x² - 7x + 3; f(2) = ?
2. f(x) = 2x² - 5x + 3; f(4) = ?
3. A quadratic function is graphed on a coordinate plane with its vertex at (2, -3) and passing through the point (4, 1). The parabola opens upward. What is the equation of this quadratic function in vertex form?

…and 5 more problems

1. A drone is flying over a park following a parabolic path described by the function h(t) = -2t² + 12t + 5, where h represents the drone's height in meters above ground level and t represents time in seconds since launch. The drone's camera can only capture objects when it is at least 15 meters above the ground. During what time interval is the drone high enough to use its camera?
2. f(x) = 2x² - 3x + 1, find f(-2) = ?
3. f(x) = 3x³ - 9x² + 5x - 7; f(3) = ?

…and 5 more problems