FUNÇÃO DO 1º GRAU: DEFINIÇÃO E GRÁFICO

Summary

In this educational video, the instructor introduces affine (or first-degree) functions, explaining their general form as y = ax + b. The video breaks down the roles of the coefficients, where 'a' is the coefficient of x (angular coefficient) and 'b' is the independent term (linear coefficient). It demonstrates how to graph such functions by calculating two points and drawing the straight line. The video also covers the significance of positive and negative values for 'a' in determining the slope of the line, as well as the intersection points with the x and y axes. The tutorial is simple, clear, and engaging for students learning the basics of affine functions.

Takeaways

• 😀 A first-degree function (or affine function) has the form f(x) = ax + b, where a and b are real numbers and a cannot be zero.
• 😀 The coefficient 'a' in the equation is called the angular coefficient, while 'b' is the independent term or linear coefficient.
• 😀 The graph of a first-degree function is always a straight line, which can be either increasing or decreasing depending on the value of 'a'.
• 😀 When the coefficient 'a' is positive, the function is increasing; when 'a' is negative, the function is decreasing.
• 😀 The intersection of the function with the X-axis is called the root or zero of the function, which occurs when y = 0.
• 😀 The intersection with the Y-axis is represented by the constant 'b' and is called the zero point or the Y-intercept.
• 😀 To graph a first-degree function, two points are enough. By selecting values for x, calculating corresponding y-values, and plotting those points, the line can be drawn.
• 😀 When given a first-degree function, the value of 'a' represents the slope, and the value of 'b' represents where the graph intersects the Y-axis.
• 😀 If no coefficient is explicitly shown for x, it is assumed to be 1. If there’s no constant term, 'b' is 0.
• 😀 To find the root of a first-degree function, set y = 0 and solve for x. This gives the point where the graph intersects the X-axis.
• 😀 It’s important to practice constructing graphs of first-degree functions by calculating the points and connecting them, which helps in visualizing how the function behaves.

Q & A

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

A first-degree function has the general form: fx = ax + b, where 'a' is the coefficient of x and 'b' is the independent term.

What are the roles of the coefficients 'a' and 'b' in a first-degree function?

'a' is called the coefficient of x and is also referred to as the angular coefficient, while 'b' is the independent term or the linear coefficient, which does not depend on the value of x.

What happens when 'a' equals zero in a first-degree function?

If 'a' equals zero, the function is no longer a first-degree function because a first-degree function requires 'a' to be non-zero.

Can you write the equation fx = ax + b in another form? What is it?

Yes, fx = ax + b can also be written as y = ax + b because fx and y are equivalent in this context.

How can we identify the coefficient of x (a) and the independent term (b) in a given equation?

The coefficient of x (a) is the number that is multiplying x, and the independent term (b) is the number that does not involve x. For example, in the equation y = 2x - 1, 'a' is 2, and 'b' is -1.

What does it mean when the function has no number in front of x, as in y = x + 2?

If there is no number explicitly written in front of x, it is implicitly understood to be 1. So, in the case of y = x + 2, 'a' is 1 and 'b' is 2.

What is the graph of a first-degree function like?

The graph of a first-degree function is a straight line, and it is always inclined. It cannot be parallel to either the X or Y axis.

How do you graph a first-degree function, such as y = 2x - 1?

To graph y = 2x - 1, you need to find at least two points by choosing values for x. For example, if x = 0, y = -1, and if x = 1, y = 1. These points (0, -1) and (1, 1) can then be plotted on the graph, and the line is drawn through them.

What is the significance of the intersection of the graph with the X-axis and Y-axis?

The intersection with the X-axis is the root of the function, where y = 0. The intersection with the Y-axis is the point where x = 0, and its value is the independent term b.

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

To find the root, set fx = 0 (or y = 0 in the equivalent form) and solve for x. For example, for y = -2x + 6, set -2x + 6 = 0, solve for x to find x = 3.