Decreasing function

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

$x<-1$

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 $x$

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