Question

Постройте график функций и опишите ее свойства y=x+3x

Answer 1

У=х+3х=4х
у=4х  - линейная функция. Графиком явл. прямая, проходящая через начало координат и точку (1,4).
Пересекает ось ОХ и ось ОУ в точке (0,0).
Функция возрастающая на всей обл. определения, то есть при х Є (-беск,+беск).
Точек экстремума нет.

Answer 2

Graph of the Function y = x + 3x

To graph the function y = x + 3x, we can simplify it by combining like terms. Adding the coefficients of x, we get y = 4x.

The graph of y = 4x is a straight line with a slope of 4 and passes through the origin (0, 0). As x increases, y increases at a faster rate due to the positive slope. Similarly, as x decreases, y decreases at a faster rate. The graph is a line that extends infinitely in both the positive and negative directions.

Properties of the Function y = x + 3x

1. Slope: The slope of the line is 4, which means that for every unit increase in x, y increases by 4 units.

2. Intercept: The line passes through the origin (0, 0), which means that when x is 0, y is also 0.

3. Direction: The line has a positive slope, indicating that it rises from left to right. As x increases, y increases.

4. Linearity: The function y = x + 3x represents a linear relationship between x and y. This means that the graph is a straight line and the rate of change of y with respect to x is constant.

Graph of y = 4x

Here is a graph of the function y = 4x:


Please note that the graph shown is a general representation of the function y = 4x and may not be to scale. The actual graph will be a straight line passing through the origin with a slope of 4.

I hope this helps! Let me know if you have any further questions.