FUNÇÃO DO 1º GRAU | COMO CONSTRUIR GRÁFICO | RAIZ DA FUNÇÃO

Summary

This engaging video script offers a comprehensive and accessible breakdown of the first-degree function in mathematics. It explains key concepts like the angular and linear coefficients, how to identify increasing and decreasing functions, and the steps to find the root of a function. The tutorial includes interactive examples, such as drawing the graph of a first-degree function by identifying where it intersects the Y and X axes. Additionally, viewers are shown how to calculate the value of f(x) for a given x, ensuring an easy-to-understand approach for students preparing for exams.

Takeaways

• 😀 Functions of the first degree are expressed as f(x) = x + b, where the highest exponent of x is 1.
• 😀 The coefficient of x is called the 'slope coefficient' (or 'angular coefficient') and determines the steepness of the function's graph.
• 😀 The constant term, b, is known as the 'linear coefficient' or 'independent term' and represents where the graph cuts the y-axis.
• 😀 f(x) is equivalent to y, so y = x + b can be used interchangeably to represent a linear function.
• 😀 The slope coefficient (a) is crucial for identifying whether a function is increasing or decreasing.
• 😀 A positive slope coefficient results in a growing (increasing) function, while a negative slope coefficient results in a shrinking (decreasing) function.
• 😀 The root of a first-degree function is the x-value where y equals 0. This is found by setting f(x) or y equal to 0 and solving for x.
• 😀 To find the root, replace y with 0, then solve for x, as shown in the examples with the functions y = x - 3 and y = -2x + 4.
• 😀 The graph of a first-degree function is a straight line, cutting the y-axis at the value of b (the linear coefficient) and the x-axis at the root.
• 😀 The slope of the function's graph determines its direction: positive slopes mean the graph ascends (increasing), while negative slopes mean the graph descends (decreasing).
• 😀 To calculate the value of f(x) for a specific x (e.g., f(10)), substitute the value of x into the function and simplify to find the result.

Q & A

What is the general form of a first-degree function?

The general form of a first-degree function is f(x) = ax + b, where 'a' is the angular coefficient and 'b' is the linear coefficient.

Why is a function called a first-degree function?

A function is called a first-degree function because the highest exponent of the variable x is 1. If the exponent were 2, it would be a second-degree function (quadratic).

What is the role of the angular coefficient in a first-degree function?

The angular coefficient (denoted as 'a') represents the slope or the rate of change of the function. It determines whether the function is increasing or decreasing.

What is the linear coefficient, and what does it represent in a first-degree function?

The linear coefficient (denoted as 'b') is the constant term that represents the value at which the function crosses the y-axis, or the y-intercept.

How can you tell if a first-degree function is increasing or decreasing?

If the angular coefficient (a) is positive, the function is increasing (the graph slopes upward). If the angular coefficient is negative, the function is decreasing (the graph slopes downward).

What is the root of a first-degree function?

The root of a first-degree function is the value of x that makes the function equal to zero, or the value where the graph intersects the x-axis.

How do you find the root of a first-degree function?

To find the root, set f(x) = 0 and solve for x. This gives the value of x where the function equals zero.

How does the graph of a first-degree function look?

The graph of a first-degree function is always a straight line. It intersects the y-axis at the value of the linear coefficient 'b' and the x-axis at the root of the function.

What happens if the angular coefficient (a) is positive in terms of the graph's direction?

If the angular coefficient 'a' is positive, the function's graph slopes upwards, meaning the function is increasing.

What is the process for graphing a first-degree function?

To graph a first-degree function, plot the y-intercept (where the function crosses the y-axis at 'b') and the root (where the function crosses the x-axis). Connect these points with a straight line.