We will say that a function is constant when, as the value of the independent variable $X$ increases, the dependent variable $Y$ remains the same.

Let's assume we have two elements $X$, which we will call $X1$ and $X2$, where the following is true: $X1, that is, $X2$ is located to the right of $X1$.

• When $X1$ is placed in the domain, the value $Y1$ is obtained.
• When $X2$ is placed in the domain, the value $Y2$ is obtained.

The function is constant when: $X2>X1$ and also \(Y2=Y1).

The function can be constant in intervals or throughout its domain.

Constant Function

## Examples with solutions for Constant Function

### Exercise #1

Determine which domain corresponds to the function described below:

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

### Step-by-Step Solution

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.

### Exercise #2

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.

### Step-by-Step Solution

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

### Exercise #3

Which domain corresponds to the described function:

The function represents the velocity of a stone after being dropped from a great height as a function of time.

### Step-by-Step Solution

According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.

In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.

Always increasing

### Exercise #4

Determine the domain of the following function:

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

### Step-by-Step Solution

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

### Exercise #5

Determine the domain of the following function:

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

### Step-by-Step Solution

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.

### Exercise #6

Determine the domain of the following function:

The function represents the weight of a person over a period of 3 years.

### Step-by-Step Solution

Logically, a person's weight is something that fluctuates.

In one week, a person's weight can increase, but in the following week, it can decrease.

Therefore, the domain that suits this function is - partly increasing and partly decreasing.

Partly increasing and partly decreasing.

### Exercise #7

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

### Step-by-Step Solution

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

Yes

### Exercise #8

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.

### Exercise #9

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.

### Exercise #10

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.

### Exercise #11

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.

### Exercise #12

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.

### Exercise #13

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.

### Exercise #14

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.

### Exercise #15

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.