Determine the domain of the following function: A function describing the charging of a computer battery during use.

Partly increasing and partly decreasing

Determine the domain of the following function: The function describes a student's grades throughout the year.

Partly increasing and partly decreasing.

Determine the domain of the following function: The function represents the weight of a person over a period of 3 years.

Partly increasing and partly decreasing.

Determine the domain of the function described below: The function represents the amount of water in a pool while it is being filled.

Partly increasing and partly decreasing

Constant Function

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: $X1<X2$ , 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

Detailed explanation

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Test yourself on increasing and decreasing intervals of a function!

Does the function in the graph decrease throughout?

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If you are interested in this article, you might also be interested in the following articles:

Graphical representation of a function

Algebraic representation of a function

Notation of a function

Domain of a function

Indefinite integral

Assignment of numerical value in a function

Variation of a function

Increasing function

Decreasing function

Functions for seventh grade

Intervals of increase and decrease of a function

In the blog of Tutorela you will find a variety of articles with interesting explanations about mathematics

Constant Function Exercises

Exercise 1

Assignment

Find the decreasing and increasing area of the function

$f(x)=5x^2-25$

Solution

In the first step, let's consider that $a=5$

Therefore $a>0$ and the parabola is at the minimum

In the second step, we find $x$ of the vertex

according to the data we know:

$a=5,b=0,c=-25$

We replace the data in the formula:

$x=\frac{-b}{2\cdot a}$

$x=\frac{-0}{2\cdot5}$

$x=\frac{-0}{10}$

$x=0$

Answer

$x<0$ Decreasing

$0<x$ Increasing

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Test your knowledge

Question 1

Is the function in the graph below decreasing?

Question 2

Is the function in the graph decreasing?

Question 3

Is the function in the graph decreasing?

Exercise 2

Assignment

Given the linear function of the graph

What is the domain of negativity of the function?

Solution

Keep in mind that the function is always above the axis: $x$

That is, the function is always positive and has no negative domain. Therefore, no $x$

Answer

The function is always positive

Exercise 3

Assignment

Find the increasing area of the function

$f(x)=6x^2-12$

Solution

In the first step, let's consider that $a=6$

Therefore $a>0$ and the parabola is a minimum

In the second step, we find $x$ of the vertex

according to the data we know that:

$a=6,b=0,c=-12$

We replace the data in the formula

$x=\frac{-b}{2\cdot a}$

$x=\frac{-0}{2\cdot6}$

$x=\frac{0}{12}$

$x=0$

Therefore

$0<x$ Increasing

$x<0$ Decreasing

Answer

$0<x$

Do you know what the answer is?

Question 1

Is the function shown in the graph below decreasing?

Question 2

Is the function shown in the graph below decreasing?

Question 3

In what domain is the function increasing?

Exercise 4

Assignment

To find the increasing and decreasing area of the function, you need to find the intersection point of the vertex

Answer

True

Exercise 5

Assignment

Given the function in the diagram, what is its domain of positivity?

Solution

Note that the entire function is always above the axis: $x$

Therefore, it will always be positive. Its area of positivity will be for all $x$

Answer

For all $x$

Check your understanding

Question 1

In what interval is the function increasing?

Purple line: $$ x=0.6 $$

Question 2

In what domain does the function increase?

Question 3

Determine in which domain the function is negative?

Examples with solutions for Constant Function

Exercise #1

Is the function shown in the graph below decreasing?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Visually inspect the graph to see if it is consistently sloping downward.
Step 2: Apply the definition of a decreasing function.

Now, let's work through each step:
Step 1: Observing the graph, the function's graph is a line moving from the top left to the bottom right. This indicates it slopes downward as we move from left to right across the $x$ -axis.
Step 2: According to the definition of a decreasing function, for any $x_1 < x_2$ , it must hold true that $f(x_1) > f(x_2)$ . Since the graph shows a line moving downward, this condition is satisfied throughout its domain.

Therefore, the function represented by the graph is indeed decreasing.

The final answer is Yes.

Answer

Yes

Exercise #2

Is the function in the graph decreasing?

Step-by-Step Solution

To analyze whether the function in the graph is decreasing, we must understand how the function's behavior is defined by its graph:

Step 1: Examine the graph. The graph presented is a horizontal line.
Step 2: Recognize the properties of a horizontal line. Horizontally aligned lines correspond to constant functions because the $y$ -value remains the same for all $x$ -values.
Step 3: Define the criteria for a function to be decreasing. A function decreases when, as $x$ increases, the value of $f(x)$ decreases.
Step 4: Apply this criterion to the horizontal line. Since the $y$ -value is constant and does not decrease as $x$ moves rightward, the function is not decreasing.

Therefore, the function represented by the graph is not decreasing.

Answer

Exercise #3

In what domain is the function increasing?

Video Solution

Step-by-Step Solution

Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.

Answer

All values of $x$

Exercise #4

In what interval is the function increasing?

Purple line: $x=0.6$

Video Solution

Step-by-Step Solution

Let's remember that a function is described as increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can see that in the domain $x < 0.6$ the function is increasing, meaning the Y values are increasing.

Answer

$x<0.6$

Exercise #5

Determine in which domain the function is negative?

Video Solution

Step-by-Step Solution

Remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can observe that in the domain $x > 1$ the function is decreasing, meaning the Y values are decreasing.

Answer

$x > 1$

Start practice

Constant Function

Test yourself on increasing and decreasing intervals of a function!

Constant Function Exercises

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Examples with solutions for Constant Function

Exercise #1

Step-by-Step Solution

Answer

Exercise #2

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Increasing and Decreasing Intervals of a Function