Constant Function

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Increasing and Decreasing Intervals of a Function
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We will say that a function is constant when, as the value of the independent variable X X increases, the dependent variable Y Y remains the same.

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

  • When X1 X1 is placed in the domain, the value Y1 Y1 is obtained.
  • When X2 X2 is placed in the domain, the value Y2Y2 is obtained.


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

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

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Test yourself on increasing and decreasing intervals of a function!

einstein

In what domain does the function increase?

–20–20–20–10–10–10101010202020–10–10–10101010000

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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)=5x2−25 f(x)=5x^2-25

Solution

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

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

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

according to the data we know:

a=5,b=0,c=−25 a=5,b=0,c=-25

We replace the data in the formula:

x=−b2⋅a x=\frac{-b}{2\cdot a}

x=−02⋅5 x=\frac{-0}{2\cdot5}

x=−010 x=\frac{-0}{10}

x=0 x=0

Answer

x<0 x<0 Decreasing

0<x 0<x Increasing

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Test your knowledge
Question 1

In what domain is the function negative?

–0.5–0.5–0.50.50.50.51111.51.51.5222000

Question 2

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

Question 3

In what domain does the function increase?

000

Exercise 2

Assignment

Given the linear function of the graph

What is the domain of negativity of the function?

the function is always above the x-axis

Solution

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

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

Answer

The function is always positive

Exercise 3

Assignment

Find the increasing area of the function

f(x)=6x2−12 f(x)=6x^2-12

Solution

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

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

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

according to the data we know that:

a=6,b=0,c=−12 a=6,b=0,c=-12

We replace the data in the formula

x=−b2⋅a x=\frac{-b}{2\cdot a}

x=−02⋅6 x=\frac{-0}{2\cdot6}

x=012 x=\frac{0}{12}

x=0 x=0

Therefore

0<x 0<x Increasing

x<0 x<0 Decreasing

Answer

0<x 0<x

Do you know what the answer is?
Question 1

What interval is the function increasing?

Purple line \( x=0.6 \)

111222333111000

Question 2

In what domain does the function increase?

Green line \( x=-0.8 \)

–2–2–2222222000

Question 3

"In which interval does the function decrease?

Red line"\( x=0.65 \)

111222333–1–1–1111000

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?

what is its domain of positivity

Solution

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

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

Answer

For all x x

Check your understanding
Question 1

In which interval does the function decrease?

The red line \( x=1.3 \)

–4–4–4–2–2–2222444666888101010–2–2–2222444000

Question 2

In what area does the function increase?

Black line.\( x=1.1 \)

–2–2–2222444666222000

Question 3

Determine the domain of the following function:

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

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