Examples with solutions for Increasing and Decreasing Intervals of a Function: Matching the graph to the story

Exercise #1

Choose the graph that best represents the following:

An aircraft's speed (Y) during landing as a function of time (X).

Step-by-Step Solution

The speed of the airplane decreases until it reaches the ground and stops (reaches 0).

Therefore, the graph will be descending until it reaches 0.

The graph shown in answer A is correct.

Answer

WeatherSpeed 000

Exercise #2

Choose the graph that best describes the following:

The acceleration of a ball (Y) after throwing it from a building as a function of time (X).

Step-by-Step Solution

Since acceleration is dependent on time, it will be constant.

The force of gravity on Earth is constant, meaning the velocity of Earth's gravity is constant and therefore the graph will be straight.

The graph that appears in answer B satisfies this.

Answer

Weather101010Speed

Exercise #3

Choose the graph that best describes the following:

Height of a basketball (Y) when a player bounces it as a function of time (X).

Step-by-Step Solution

When the player dribbles the ball, it starts from hand height, touches the floor, and so on.

In other words, the ball starts from a height, touches the floor at height 0, and returns to the player's hand.

This means the graph will have an up and down motion, therefore the graph in answer B is correct.

Answer

Weather101010Height

Exercise #4

Choose the graph that best represents the following:

Height of a child (Y) when jumping on a trampoline as a function of time (X).

Step-by-Step Solution

When the child jumps on the trampoline, their height changes. At the peak of the jump, they are at the highest point, and then they land back down to a lower height.

In other words, the action repeats itself, and the graph we'll see will show ups and downs. Therefore, the graph in answer A is the correct one.

Answer

Weather101010Height

Exercise #5

Choose the graph that best describes the following:

A sprinter who runs at a certain speed (Y) and gradually gets tired over time (X).

Step-by-Step Solution

The runner starts at a high speed and as time passes, he loses his strength and runs slower.

In other words, the graph will be descending, and therefore answer C is correct.

Answer

WeatherSpeed 000

Exercise #6

Choose the graph that best describes the following:

The speed of a car (Y) as it travels at a constant speed as a function of time (X).

Step-by-Step Solution

Since the car's speed is constant and does not change throughout the journey, the graph will be constant.

The graph shown in answer D describes this correctly.

Answer

WeatherSpeed 000

Exercise #7

Choose the graph that best describes the following:

Amount of fuel in a car (Y) while driving as a function of time (X).

Step-by-Step Solution

Since the vehicle uses fuel for engine operation, the fuel decreases over time.

The more the vehicle travels, the more the amount of fuel decreases.

The graph that correctly describes this is B.

Answer

WeatherAmount of fuel000

Exercise #8

Choose the graph that best describes the following:

Temperature of hot water (Y) placed on a table at room temperature as a function of time (X).

Step-by-Step Solution

The temperature of hot water is about 80 degrees.

Room temperature is about 25 degrees.

Therefore, the graph we will see will have a downward trend, and at the end of the time, the value will be above the X-axis (since the room is not frozen, the temperature will not reach freezing point)

The graph that describes this is graph C.

Answer

WeatherTemperature'000

Exercise #9

Choose the graph that represents the following:

The length of a burning candle (Y) according to burning time (X).

Step-by-Step Solution

Since the velocity is directly proportional to the acceleration, and since the acceleration is constant, the graph must be a straight line.

The sketch that describes this is sketch D.

Answer

WeatherSail length000

Exercise #10

Choose the graph that best describes the following:

The velocity of a heavy stone (Y) after being dropped from a great height as a function of time (X).

Step-by-Step Solution

Since the velocity depends on the acceleration in a direct relationship, and since the acceleration is constant, the graph must have a straight slope.

Since the graph in answer D describes a constant function, this is the correct answer.

Answer

WeatherSpeed 000

Exercise #11

Choose the graph that best represents the following:

Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).

Step-by-Step Solution

Since the freezing point of water is below 0, the temperature of the water must drop below 0.

The graph in answer B describes a decreasing function and therefore this is the correct answer.

Answer

WeatherTemperature'000