**We will say that a function is decreasing when, as the value of the independent variable** **$X$**** increases, the value of the function** **$Y$**** decreases.**

**We will say that a function is decreasing when, as the value of the independent variable** **$X$**** increases, the value of the function** **$Y$**** decreases.**

In what domain does the function increase?

Let's assume we have two elements $X$, which we will call $X1$ and $X2$, where the following is true: X1<X2, meaning, 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 decreasing when:** **$X2>X1$**** and also** **$Y2<Y1$****.**

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

**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

Constant 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**

**Assignment**

Find the decreasing area of the function

$y=(x+1)+1$

Solution

$a$ coefficient of $x^2$

Therefore $0<a$

is the minimum point

The vertex of the function is $\left(-1,1\right)$

The function decreases in the area of $x<-1$

**Answer**

$x<-1$

Test your knowledge

Question 1

In what domain is the function negative?

Question 2

In what domain is the function increasing?

Question 3

In what domain does the function increase?

**Assignment**

Given the function in the graph

When is the function positive?

**Solution**

The intersection point with the axis :$x$ is: $\left(-4,0\right)$

First positive, then negative.

Therefore $x<-4$

**Answer**

$x<-4$

**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 $x$

Do you know what the answer is?

Question 1

What interval is the function increasing?

Purple line \( x=0.6 \)

Question 2

Determine the domain of the following function:

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

Question 3

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.

**Assignment**

Given the function in the diagram

What are the areas of positivity and negativity of the function?

**Solution**

Let's remember that a function is positive when it is above the axis: $x$ and the function is negative when it is below the axis $x$

Given that the point of intersection with the axis: $x$ is $\left(3.5,0\right)$

When $x>3.5$ it is below: $x$

When $x<3.5$ it is above: $x$

Therefore, the function is positive when $x<3.5$ and negative when $x>3.5$

**Answer**

Positive when $x<3.5$

Negative when $x>3.5$

**Assignment**

Find the increasing and decreasing area of the function

$f(x)=-2x^2+10$

**Solution**

In the first step, let's consider that $a=-2$

Therefore$x<0$ and the parabola is at its maximum

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

according to the data we know

$a=-2,b=0,c=10$

We replace the data in the formula

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

$x=\frac{-0}{2\cdot\left(-2\right)}$

$x=\frac{-0}{-4}$

$x=0$

Then we know that: $x=0$ and we replace it in the function and find that $y$

$y=10$

**Answer**

$0<x$ Decreasing

$x<0$ Increasing

Check your understanding

Question 1

Determine which domain corresponds to the function described below:

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

Question 2

Determine which domain corresponds to the described function:

The function represents the amount of water in a pool while it is being filled.

Question 3

Determine which domain corresponds to the described function:

The function describes a person's energy level throughout the day.

Related Subjects

- Linear Function
- Graphical Representation of a Function that Represents Direct Proportionality
- The Linear Function y=mx+b
- Finding a Linear Equation
- Positive and Negativity of a Linear Function
- Representation of Phenomena Using Linear Functions
- Factorization: Common factor extraction
- Inequalities
- Inequalities with Absolute Value
- The Extended Distributive Property
- Algebraic Method
- Ordered pair
- Graph
- Value Table
- Reading Graphs
- Continuous graph
- Discrete graph
- Domain of a Function
- Rate of Change of a Function
- Variation of a Function
- Absolute Value
- Absolute Value Inequalities
- Notation of a Function