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 $X$.

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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

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Exercises on the variation of a function

Exercise 1

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

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

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Question 1

Given the following graph, determine whether the rate of change is uniform or not