Function Notation Worksheets Grade 9

1. Isabella is a materials engineer testing the thermal expansion of a metal rod. The length L of the rod in millimeters after being heated to a temperature T degrees Celsius is modeled by the function L(T) = 250 + 0.027T + 0.00012T². The testing protocol requires her to measure the rod's length when the temperature reaches exactly 70°C. What is L(70)?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). The function f(x) = √(x² + 9) represents the distance from the point (0,0) to any point (x,3) along the vertical line x = 4. Evaluate f(4) to find the length of the hypotenuse of this triangle.
3. f(x) = 3x² - 2x + 7, f(-2) = ?

…and 4 more problems

1. Noah is analyzing the profit from his online tutoring business. The daily profit in dollars, P(h), is modeled by the function P(h) = -3h² + 51h - 36, where h represents the number of hours he tutors each day. Due to a scheduling change, Noah tutors for 6 hours today. What is P(6)?
2. A local tech company is modeling the profit from their new smartphone app using the function P(x) = -0.02x² + 50x - 800, where x represents the number of app downloads and P(x) represents the profit in dollars. The company wants to determine their profit when they reach 1,200 downloads. Calculate P(1200) to find the profit at this download level.
3. f(x) = 2x² - 5x + 3, f(3) = ?

…and 5 more problems

1. Mason is tracking the fuel efficiency of his motorcycle. The distance traveled in kilometers after t hours is modeled by the function D(t) = 72t - 2t². How far does Mason travel after exactly 7 hours?
2. A graph on a coordinate plane shows the function f(x) = -3x^2 + 15x - 11. Aroha draws a vertical line at x = 7 and marks the point where it meets the curve. Evaluate f(7) to find the y-coordinate of that point.
3. Mason is analyzing the speed of a particle moving along a straight line. The velocity of the particle, in meters per second, at time t seconds is given by the function v(t) = 2t² - 17t + 27. Mason needs to determine the velocity of the particle exactly 7 seconds after it starts moving. What is v(7)?

…and 6 more problems