Composition of Functions and Modeling Answers

On a coordinate plane, f (x) goes through (negative 5, 6), has a vertex at (0, 1), and goes through (5, 6). G (x) has 2 curves. A curve opens up and to the right in quadrant 1 and approaches the y-axis and x-axis. A curves opens down and to the left in quadrant 3 and approaches the y-axis and x-axis.

Consider the composite function .If f(x) = 3x2, what is g(x)?

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to of its maximum volume? Use π = 3.14 and .

The Brazilian free-tailed bat can travel 99 miles per hour. After sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. How long before these bats cover an area of 80,000 square miles? Use π = 3.14.

Ana is purchasing new furniture and must pay a 10% sales tax. She can have the furniture delivered for an additional $25 fee that is not taxed. Which function represents the amount Ana will pay for furniture with a pretax price of x dollars?

Suppose f(x) = (5 – x)3 and, g(x) = a + x2, and f(g(x)) = (1 – x2)3. What is the value of a?

The function represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

When Jose installs a new app on his phone, it creates a square icon on his home screen. The square starts with side lengths of 1 cm. The side lengths grow by 2.8 cm each second until the square reaches its maximum size. What is the perimeter of the square after 1.5 seconds? Recall that the perimeter of a shape is the sum of its side lengths.

On a coordinate plane, f (x) curves up through (negative 2, negative 3), has an inflection point at (0, 0), and curves up through (2, 3). G (x) has 2 curves. A curve opens up and to the right in quadrant 1 and approaches the y-axis and x-axis. A curves opens down and to the left in quadrant 3 and approaches the y-axis and x-axis.

A 2000-kilogram sports car accelerates at a rate of 30 meters per second squared. The velocity of the car is v = at, where a is acceleration in meters per second squared, and t is time in seconds. The kinetic energy of the car is , where m is the mass in kilograms.Which function represents the kinetic energy of the car after accelerating for t seconds?