Unit Test — Unit test Answers

The force exerted by a pulley is the sum of the tension and the force of gravity. Since a pulley is used to lift something, the force is negative. The tables show the tension, T(m), and the force of gravity, G(m), for objects of various masses, m in grams, all accelerating upward at 2.5 m/s2.The force of the rope is equal to the negative of the sum of the rope’s tension and the force of gravity.

The table shows three functions and their output values for different values of x.

The graph of f(x) is shown below.If f(x) and its inverse function, , are both plotted on the same coordinate plane, where is their point of intersection?

The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is used to determine the height of the ball depending on its distance from the goalie, x.

Which graph represents the same relation as the table below?xf(x)–25011–12–3

The function f(x) = 16.4x + 2 is used by a construction company to estimate the amount of fuel necessary for a truck to get to a job site depending on the miles from the office, x. The mathematical domain for the function is the set of real numbers.

The length of time in hours of two airplane flights are represented by the following functions, where x is the number of miles for the flight:Flight A: f(x) = 0.003x – 1.2Flight B: g(x) = 0.0015x + 0.8Which function represents the total of the flight times, h(x) = f(x) + g(x)?

Given , find f(7).

The dimensions of a rectangle are represented by the functions shown.

If h(x) is the inverse of f(x), what is the value of h(f(x))?

Given and , for which value of does ?

Which function has an inverse that is also a function?

What is the value of the following function when x = 0?

Study the equations:f(x) = 6x + 7g(x) = 4x – 2What is h(x) = f(x)g(x)?

The functions below represent the amounts of water released from two reservoirs over x weeks:Reservoir Af(x) = x2 – 7x + 5Reservoir Bg(x) = 3x2 – 6x + 2The function h(x) = f(x) – g(x) represents the difference in the amounts of water released.Determine which statements about h(x) and about the reservoirs are true. Check all that apply.h(x) = –2x2 – 13x + 6h(x) = –2x2 – x + 3Reservoir A releases less water than Reservoir B over 1 week.Reservoir A releases the same amount of water as Reservoir B over 1 week.Reservoir A releases more water than Reservoir B over 1 week.

To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function. Is Shayla applying the vertical line test correctly?

If , what is ?

A toy company is releasing a new catapult for water balloons that launches them at 9.8 meters per second from a stand 0.6 meters tall. The function f(x) = −4.9x2 + 9.8x + 0.6 describes the path of the water balloon, where x is the amount of time since the launch.

Which graph shows h(x) = (f(x))(g(x))?

Which table represents the same relation as the set ?