Variation of a Function

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 $X$.

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

Assignment

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

Solution

$a$ coefficient of $x^2$

Given in the exercise: $-5$

$b$ coefficient of $x$

Given in the exercise: $1$

$c$ is a free number

Therefore it is: $0$

Answer

$a=-5,~b=1,~c=0$

Assignment

Given the linear function in the graph

When is the function positive?

Solution

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

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

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

Answer

$x\gt2$

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

$y=-40x+40$

Solution

$a$ coefficient of $x^2$

Given in the exercise: $0$

$b$ coefficient of $x$

Given in the exercise: $-40$

$c$ is a free number

Therefore it is: $40$

Answer

$a=0,~b=-40,~c=40$

Assignment

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

Solution

$a$ coefficient of $x^2$

Given in the exercise: $-1$

$b$ coefficient of $x$

Given in the exercise: $3$

$c$ is a free number

Therefore it is: $40$

Answer

$a=-1,~b=3,~c=40$