Question

дана квадратичная функция y+3x^2,  где х целое число и -4 < 0 < 2. составь таблицу соответствующих значений переменных х и у и запиши область определения и множество значений этой функции путем перечисления элементов этих множеств.

Answer 1

Quadratic Function and Table of Values

The given quadratic function is y = 3x^2, where x is an integer and -4 < x < 2. We need to create a table of corresponding values for x and y and determine the domain and range of this function.

To create the table of values, we can substitute different values of x into the equation and calculate the corresponding y values. Let's calculate the values for x ranging from -4 to 1:

| x | y | |---|---| | -4 | 48 | | -3 | 27 | | -2 | 12 | | -1 | 3 | | 0 | 0 | | 1 | 3 |

Now, let's determine the domain and range of this function.

Domain and Range

The domain of a function refers to the set of all possible input values (independent variable), while the range refers to the set of all possible output values (dependent variable).

For the given quadratic function y = 3x^2, the domain is defined as all possible values of x. In this case, the domain is -4 < x < 2.

The range of the function can be determined by analyzing the shape of the quadratic curve. Since the coefficient of x^2 is positive (3), the parabola opens upwards. This means that the minimum value of y occurs at the vertex of the parabola, and there is no maximum value. Therefore, the range of the function is y ≥ 0.

To summarize: - Domain: -4 < x < 2 - Range: y ≥ 0

Please let me know if there's anything else I can help you with!