FUNÇÃO AFIM - EXERCÍCIOS # 1

Summary

In this educational video on first-degree (affine) functions, the instructor explains key concepts such as the general form of a first-degree function, how to determine values for constants like k, and the conditions for the function to be increasing. Practical examples are provided, including determining values of k in specific equations and understanding the difference between linear and affine functions. The video also covers graphing methods, emphasizing how to plot first-degree functions using points of intersection with the x and y axes. The session concludes with encouragement for viewers to engage with the content and continue learning.

Takeaways

• 😀 A first-degree (affine) function is in the form Y = Ax + B, where A cannot be zero.
• 😀 The term 'first-degree' refers to the highest power of the variable x in the function, which is 1.
• 😀 To make sure the function is in the first-degree form, ensure that the coefficient of x (A) is non-zero.
• 😀 In the example 2K - 1, we solve for k to ensure the function is first-degree: 2K must not equal 1, so k cannot be 1/2.
• 😀 To ensure a function is in the first-degree form, set expressions like k + 2 = 0, which gives k = -2.
• 😀 For a function to be increasing, the coefficient of x (A) must be positive (A > 0).
• 😀 In the inequality for an increasing function, solving 3k - 6 > 0 leads to k < 2.
• 😀 A linear function is a first-degree function where the constant term B equals zero (i.e., Y = Ax).
• 😀 To find the value of the coefficient A in a linear function, substitute given points into the equation and solve for A.
• 😀 Graphing a first-degree function involves selecting two x-values, calculating the corresponding y-values, and plotting the points to form a straight line.

Q & A

What is a first-degree function?

A first-degree function, also known as an affine function, has the format Y = Ax + B, where A and B are constants, and A cannot be zero.

Why is a function with the form Y = Ax + B called a first-degree function?

It is called a first-degree function because the highest power of the variable x is 1, which means it is a first-degree polynomial.

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

The coefficient 'A' in a first-degree function is the slope of the line. It indicates the rate of change of Y with respect to X, and it cannot be zero.

Why can't the coefficient 'A' be zero in a first-degree function?

If the coefficient 'A' is zero, the equation would no longer be linear (it would become a constant function, Y = B), meaning there is no slope and no dependence on X.

How do you determine the value of K in the equation 2K - 1 so that it represents a first-degree function?

For the equation 2K - 1 to be in the form of a first-degree function, K must be different from 1/2 because if K equals 1/2, the coefficient of x would be zero, making it not a first-degree function.

What condition makes a first-degree function increasing?

A first-degree function is increasing when the coefficient 'A' is positive. This means that the slope of the line is positive, and as X increases, Y also increases.

In the equation Y = 17 - 3K - 6x, how do you determine the value of K for the function to be increasing?

To make the function increasing, solve the inequality -3K - 6 > 0, which simplifies to K < 2. Therefore, the value of K must be less than 2.

What is the difference between a first-degree function and a linear function?

A first-degree function has the general form Y = Ax + B, while a linear function is a special case where B = 0, meaning the function passes through the origin and can be written as Y = Ax.

How do you find the value of 'A' in a linear function that passes through the point (3, 2)?

To find 'A', substitute the point (3, 2) into the equation Y = Ax. By substituting X = 3 and Y = 2, you get 2 = 3A. Solving for A gives A = 2/3.

What is the importance of the root of a first-degree function in graphing it?

The root of a first-degree function is the X-value where the function intersects the X-axis (i.e., where Y = 0). This is important for graphing because it helps identify where the function crosses the axis and gives a point for the graph.