Functions - Examples, Exercises and Solutions

Determine the domain of the following function:

The function describes a student's grades throughout the year.

According to logic, the student's grades throughout the year depend on many criteria that are not given to us.

Therefore, the appropriate domain for the function is - it is impossible to know.

Impossible to know.

Determine the domain of the following function:

A function describing the charging of a computer battery during use.

According to logic, the computer's battery during use will always decrease since the battery serves as an energy source for the computer.

Therefore, the domain that suits this function is - always decreasing.

Always decreasing

Determine which domain corresponds to the function described below:

The function represents the height of a child from birth to first grade.

According to logic, a child's height from birth until first grade will always be increasing as the child grows.

Therefore, the domain that suits this function is - always increasing.

Always increasing.

Determine which domain corresponds to the function described below:

The function represents the amount of fuel in a car's tank according to the distance traveled by the car.

According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.

Therefore, the domain that is suitable for this function is - always decreasing.

Always decreasing

Choose the graph that best represents the following:

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

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.

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).

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.

Choose the graph that best describes the following:

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

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.

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).

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.

Choose the graph that best describes the following:

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

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.

Choose the graph that represents the following:

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

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.

Choose the graph that best represents the following:

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

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.

Is it possible to create an increasing function with the two given points?

We will begin by connecting the two points to each other, and subsequently we should see that we have obtained an increasing function.

Yes

Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.

For each number, multiply by$(-1)$.

The function is:

$f(x)=(-1)x$

Let's start by assuming that x equals 0:

$f(0)=(-1)\times0=0$

Now let's assume that x equals minus 1:

$f(-1)=(-1)\times(-1)=1$

Now let's assume that x equals 1:

$f(1)=(-1)\times1=-1$

Now let's assume that x equals 2:

$f(2)=(-1)\times2=-2$

Let's plot all the points on the function graph:

We can see that the function we got is a decreasing function.

Decreasing

Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.

For each number, multiply by 0.

The function is:

$f(x)=x\times0$

Let's start by assuming that x equals 0:

$f(0)=0\times0=0$

Now let's assume that x equals 1:

$f(1)=1\times0=0$

Now let's assume that x equals -1:

$f(-1)=(-1)\times0=0$

Now let's assume that x equals 2:

$f(2)=2\times0=0$

Let's plot all the points on the function's graph:

We can see that the function we obtained is a constant function.

Constant

Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table:

Each number is divided by $(-1)$.

The function is:

$f(x)=\frac{x}{-1}$

Let's start by assuming that x equals 0:

$f(0)=\frac{0}{-1}=0$

Now let's assume that x equals 1:

$f(1)=\frac{1}{-1}=-1$

Now let's assume that x equals 2:

$f(-1)=\frac{-1}{-1}=1$

Let's plot all the points on the function graph:

We see that we got a decreasing function.

Decreasing