Composition of Functions and Modeling Answers

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.

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.

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?

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

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.

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.

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

A marble dropped in still water will create circular ripples or waves. The radius of each circular wave will increase 4 centimeters per second. What is the circumference of the circle after t seconds?

Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?Use SA=4πr2.