Variation of a Function

🏆Practice variation of a function

The variation of a function means the rate at which a certain function changes. The rate of variation of a function is also called the slope.

According to the mathematical definition, the slope represents the change of the function (Y) (Y) by increasing the value of X X by 1 1 .

  • If the function's graph is represented by a straight line, it means that the rate of variation of the function is constant
  • However, if the graph is not represented by a straight line, this implies that the rate of variation of the function is not constant
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Given the following graph, determine whether function is constant

–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666000

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That is, there are functions, such as the linear function (which we will study in more detail later, but generally speaking, it is a function with the variable to the first power) in which the slope, or in other words, the rate of change of the function is constant, and there are other functions that may have an increasing or decreasing rate of change that is calculated separately for each value X X .


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

Functions for seventh grade

Graphical representation of a function

Algebraic representation of a function

Function notation

Domain of a function

Indefinite integral

Assignment of numerical value in a function

Increasing function

Decreasing function

Constant 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


Exercises on the variation of a function

Exercise 1

Assignment

y=5x2+x y=-5x^{2}+x

Solution

a a coefficient of x2 x^2

Given in the exercise: 5 -5

b b coefficient of x x

Given in the exercise: 1 1

c c is a free number

Therefore it is: 0 0

Answer

a=5, b=1, c=0 a=-5,~b=1,~c=0


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Exercise 2

Assignment

Given the linear function in the graph

When is the function positive?

Exercise 2 - Given the linear function in the graph

Solution

The function is positive when it is above the axis: x x

Pay attention that the intersection point with the axis x x is (2,0) \left(2,0\right)

According to the graph, the function is positive, therefore x>2 x\gt2

Answer

x>2 x\gt2


Exercise 3

Assignment

Given the function in the graph

When is the function positive?

When is the function positive

Solution

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

First positive, then negative.

Therefore x<4 x<-4

Answer

x<4 x<-4


Do you know what the answer is?

Exercise 4

Assignment

y=40x+40 y=-40x+40

Solution

a a coefficient of x2 x^2

Given in the exercise: 0 0

b b coefficient of x x

Given in the exercise: 40 -40

c c is a free number

Therefore it is: 40 40

Answer

a=0, b=40, c=40 a=0,~b=-40,~c=40


Exercise 5

Assignment

y=x2+3x+40 y=-x^{2}+3x+40

Solution

a a coefficient of x2 x^2

Given in the exercise: 1 -1

b b coefficient of x x

Given in the exercise: 3 3

c c is a free number

Therefore it is: 40 40

Answer

a=1, b=3, c=40 a=-1,~b=3,~c=40


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