An first degree function is one whose formation law can be written as follows:
y = ax + b
In which, a and b belong to the set of real numbers, and a is nonzero. This kind of occupation is also called affine function.
It is important to remember the main concepts about functions in general to fully understand the functionsoffirstdegree.
What is a function?
An occupation is a mathematical rule that relates each element x, of a set A, to a single element y, of a set B. Sets A and B are known, respectively, as domain and counter-domain. x and y are known, respectively, as independent variable and dependent variable, because the value of y will always depend on the value of x.
So, the functionsoffirstdegreeare rules that relate each element of a set to a single element of another. whose independent variable is a potency of exponent 1. the degree of a occupation it is always given by the largest exponent of the independent variable, and in the case of first-degree functions, the largest exponent is 1.
Mind Map: 1st Degree Function Chart
* To download the mind map in PDF, Click here!
First Degree Function Examples
The following examples are from functionsoffirstdegree. This means that they can be written in the form y = ax + b, or they are already in that form.
a) y = 2x + 9. this is a occupationto, or of the first degree, where a = 2 and b = 9.
b) y = – x – 7. Although the sign of – 7 is not positive, this is also a occupationoffirstdegree, with a = – 1 and b = – 7. So that there is no doubt, just write it: y = (–1)x + (–7).
c) f(x) = 0.2x. this is a occupationto, or of the first degree, where a = 0.2 and b = 0. Note that f(x) is another notation for y, but they both represent the same thing.
From the examples above, always remember: the functions of the first degree are those where the independent variable has a maximum exponent equal to 1.
Examples of non-first degree functions
For the avoidance of doubt, look now at some examples of functionsthat are not of the firstdegree:
a) y = 2x2. That occupation it is not of the first degree because the independent variable has degree 2. In this case, it is a function of the second degree.
b) y = 1/x. That occupation is not first degree because y = 1/x can also be written as y = x-1 and this (-1) is not the correct exponent for the first degree functions.
First degree function graph
All occupationoffirstdegree can be represented geometrically by a straight. To build it, just find two ordered pairs of points that belong to this line, place them on the Cartesian plane and trace the straight that passes through them. taking the occupation y = x – 3 as an example, the step-by-step construction of the graph of a function of the first degree should be as follows:
1st Find the ordered pairs
To find them, just choose any two values for the independent variable and find their counterparts using the occupation. For this, we choose x = 1 and x = 2 and build the following table:
x |
y = x – 3 |
y |
Ordered pair (x, y) |
1 |
y = 1 – 3 = – 2 |
– 2 |
(1, –2) |
2 |
y = 2 - 3 = 0 |
– 1 |
(2, –1) |
The second column of this table is filled with the value of x substituted in the occupation, the third with the final value of y and the fourth with the ordered pair formed by the values of x and y.
2nd Place the ordered pairs on the Cartesian plane and draw the line that contains them
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-funcao-primeiro-grau.htm
