Taxa de Variação da Função Afim

Summary

In this lesson, the instructor explains how to calculate the rate of variation of a function, focusing on the concept of the angular coefficient or slope. By using simple examples, the video demonstrates how to compute this rate using the formula Δy/Δx, where y represents the vertical change and x represents the horizontal change between two points on the graph. The lesson emphasizes understanding the concept of rate of variation and its importance in linear functions, helping students grasp how to interpret and calculate the function’s rate of change in a straightforward manner.

Takeaways

• 😀 The rate of variation is another name for the angular coefficient of a linear function.
• 😀 The rate of variation determines the slope or degree of inclination of the line representing a function's graph.
• 😀 The rate of variation can be calculated using the formula Δy/Δx, which measures the change in y over the change in x.
• 😀 The symbol Δ (delta) indicates variation or change in mathematics.
• 😀 To find the rate of variation, subtract the y-values and x-values of two points on the function's graph and then divide them.
• 😀 An example was provided where a line passes through the points (1, 3) and (4, 15), showing how to calculate the rate of variation.
• 😀 The formula for calculating the rate of variation is simply Δy/Δx, which involves subtracting y2 from y1 and x2 from x1.
• 😀 In the example, the result of the rate of variation was 12/3 = 4, which represents the angular coefficient of the line.
• 😀 Another example was given to calculate the rate of variation where y-values and x-values were given as 3 and 1 for x and 1 and 10 for y, respectively.
• 😀 The key takeaway is that understanding the rate of variation (angular coefficient) is essential for analyzing the slope of any affine function.

Q & A

What is the rate of variation of a function?

The rate of variation, also known as the angular coefficient, refers to the degree of inclination of the line representing the graph of a function. It is calculated as the change in the dependent variable (y) divided by the change in the independent variable (x), represented by the formula Δy/Δx.

What is the formula for calculating the rate of variation?

The formula for calculating the rate of variation is Δy/Δx, which is the change in y divided by the change in x. It is calculated using the formula: (y2 - y1) / (x2 - x1).

What do Δy and Δx represent in the rate of variation formula?

In the formula Δy/Δx, Δy represents the change in the dependent variable (y), and Δx represents the change in the independent variable (x).

How does the rate of variation affect the graph of a function?

The rate of variation determines the slope or angle of the line on the graph of the function. A larger rate of variation results in a steeper line, while a smaller rate of variation indicates a less steep line.

What is the relationship between the rate of variation and the angular coefficient?

The rate of variation is also called the angular coefficient, and they are essentially the same concept. Both terms refer to the slope or incline of the line that represents the graph of the function.

Why is it important to know how to calculate the rate of variation?

Knowing how to calculate the rate of variation is important because it helps in understanding the behavior of the function's graph. It allows us to determine how changes in the input (x) affect the output (y).

What is the significance of the linear coefficient in an affine function?

The linear coefficient in an affine function is related to the rate of variation, as it influences the slope of the graph. It helps determine the direction and steepness of the line that represents the function.

What does the term 'affine function' refer to in this context?

An affine function is a function that can be represented by a straight line. Its general form is f(x) = mx + b, where m is the slope (rate of variation) and b is the y-intercept.

Can you give an example of how to calculate the rate of variation?

Sure! For two points (1, 3) and (4, 15), the rate of variation is calculated as follows: Δy = 15 - 3 = 12 and Δx = 4 - 1 = 3. The rate of variation is then 12 / 3 = 4.

How do you calculate the rate of variation when the points are (1, 3) and (10, 1)?

To calculate the rate of variation, use the formula: Δy = 1 - 3 = -2 and Δx = 10 - 1 = 9. The rate of variation is then -2 / 9, which is approximately -0.22.