Concepts and Applications of Functions

Two interlocking gears and have and teeth, respectively. The gear rotates times while rotates times. When the number of teeth of gear is , how many times does gear rotate?

For a function , let and . Find the value of .

A supermarket sells apple for dollars per . When the price of of apple is dollars, find the price of of apple.

A bathtub can hold of water. After filling water in the empty bathtub, of water was filled in minutes. When we assume the amount of water filled after minutes to be , how long does it take to fill the bathtub to the full?

There is a candle that loses its length by every minute after it was lit. For a candle just lit with remaining length , how long does it take until the candle is gone?

As shown below, point and are on the graph and respectively, and the coordinate of point is . When square is in the first quadrant, find the length of the side of the square . (Here, the four sides of the square are parallel to the -axis or -axis.)

For two intermeshing gears and with and teeth, respectively, the gear rotates times while rotates times. How many times does rotate during rotates times?

Tyra planned to visit her grandparents by car for thanksgiving holiday. The figure shown below displays the relation between the speed of car and the estimated time to arrival . If it took hours for her to get to her grandparents' house, find how fast she drove the car in average.

For a function , let . Find the value of .

If the -coordinate of the point on the graph of and the point on the graph of are both as shown below, what is the area of the triangle ?

Below is the inversely proportional graph , and the two points and are on the graph. The four sides of the rectangle are parallel to the -axis or -axis. Find the area of . (Here, is a constant.)

Below is the inversely proportional graph , where point is on the first quadrant of the graph. What is the area of the rectangle ? (Here, is the origin.)

A fish tank can be filled up with water after minutes if one fills of water per minute. When minutes is taken to fill it up by per minute, find the relationship between and .

The volume of gas is inversely proportional to the pressure atm under constant temperature. The volume of a gas was under the atmospheric pressure atm. When the atmospheric pressure is atm, find the volume of this gas. (Note, atm is a measure of atmospheric pressure.)

For a triangle of area shown in the figure below, the length of base is , and the height is . When , find the value of .

If you draw a straight line parallel to the -axis from point in the first quadrant of graph until it intersects graph and label it as point , then draw a line parallel to the -axis from point until it intersects graph and label it as , what is the area of triangle ?

For functions and , find the value of .

There is a right triangle with and as shown in the figure below. For point moving on the side , the length of segment is , and the area of triangle is . When , find the length of .

When trying to distribute pieces of candy to people, pieces each, find the relationship between and .