# Constant Function

🏆Practice increasing and decreasing intervals of a 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, 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. ## Test yourself on increasing and decreasing intervals of a function! In what interval is the function increasing? Purple line: \( x=0.6$$

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

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:

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

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

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

$x=0$

$x<0$ Decreasing

$0 Increasing

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### 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 $x$

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 Increasing

$x<0$ Decreasing

$0

Do you know what the answer is?

### Exercise 4

Assignment

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

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 $x$

For all $x$