RÁPIDO e FÁCIL | COMO CONSTRUIR GRÁFICO DA FUNÇÃO DO 1º GRAU

Summary

This video explains how to graph a first-degree function in just two simple steps. The first step is to find the root of the function, which is where the graph intersects the X-axis. The second step is identifying the Y-intercept, where the graph crosses the Y-axis. By following these steps, the user can quickly sketch the graph by determining just two key points. Examples are provided, demonstrating how to apply this method to different functions. The video emphasizes the simplicity of this process, encouraging viewers to master graphing linear functions efficiently.

Takeaways

• 😀 The first step to graphing a linear function is to find its root (the x-value where y equals 0).
• 😀 To find the root of a function, set y = 0 and solve for x.
• 😀 The second step is to identify where the graph intersects the y-axis, which occurs at the value of the constant term (B) in the linear equation.
• 😀 The root of a function represents the point where the graph intersects the x-axis.
• 😀 The value of the constant term (B) represents the point where the graph intersects the y-axis.
• 😀 When graphing, only two points are needed to draw the line: the root and the y-intercept.
• 😀 For the function f(x) = -x + 3, the root is 3, and the y-intercept is also 3, so the graph intersects both axes at this point.
• 😀 A function with a negative coefficient (like f(x) = -x + 3) will have a decreasing graph (goes downhill).
• 😀 The process to find the root involves setting y = 0, isolating x, and solving for its value.
• 😀 The graph of a first-degree function is always a straight line, and its slope indicates whether the graph is increasing or decreasing.
• 😀 Understanding the slope and intercept of a function can help in sketching its graph quickly and efficiently.

Q & A

What is the first step in constructing a graph of a first-degree function?

The first step is to find the root of the function, which is the value of x that makes the function equal to zero.

How do you find the root of a function?

To find the root, set y equal to zero and solve for x. The value of x that satisfies the equation will be the root.

What does the graph of a first-degree function look like?

The graph of a first-degree function is a straight line, and it cuts the Y-axis at the value of the constant term (B), and it cuts the X-axis at the root of the function.

What happens when you find the root of a first-degree function?

When you find the root, the graph will intersect the X-axis at that value, indicating where y equals zero.

Where does the graph of a first-degree function intersect the Y-axis?

The graph of the first-degree function intersects the Y-axis at the value of the constant term, which is represented by B in the equation.

What is the significance of the constant term in a first-degree function?

The constant term in the equation is where the graph cuts the Y-axis, representing the value of y when x equals zero.

What should you do after finding the root and the Y-intercept?

Once you know the root and the Y-intercept, you can plot these two points on the graph, and the graph will be a straight line passing through them.

How can you determine whether a function is increasing or decreasing based on the graph?

If the graph is sloping upwards from left to right, the function is increasing. If the graph slopes downwards, the function is decreasing.

What happens if the coefficient of x (a) is negative?

If the coefficient of x is negative, the graph will be decreasing, meaning it will slope downwards from left to right.

Can you construct a graph of a first-degree function with just two points?

Yes, by knowing the root and the Y-intercept, you only need these two points to construct the graph, as the graph is a straight line connecting them.