Question

Y=x^2-7 найдите множество значений функции

Answer 1

Y=[-7;+∞)
готово всегда пожалуйста
PS скобки проставить так как показано

Answer 2

To find the range (or set of values) of the function $y = x^2 - 7$, we need to determine the possible output values (y-values) that the function can take for different inputs (x-values).

The given function is a quadratic function in the form of $y = ax^2 + bx + c$, where $a = 1$, $b = 0$, and $c = -7$.

A quadratic function is a parabola that opens either upwards or downwards. Since the coefficient of $x^2$ is positive (1 in this case), the parabola opens upwards. This means that the minimum value of the function occurs at the vertex of the parabola.

The x-coordinate of the vertex of a parabola in the form $y = ax^2 + bx + c$ is given by $-\frac{b}{2a}$. In this case, $b = 0$ and $a = 1$, so the x-coordinate of the vertex is $x = -\frac{0}{2 \cdot 1} = 0$.

Now, substitute $x = 0$ into the function to find the y-coordinate of the vertex:

$y = 0^2 - 7 = -7$

So, the vertex of the parabola is at the point (0, -7).

Since the parabola opens upwards, the range of the function is all the y-values greater than or equal to the y-coordinate of the vertex. Therefore, the range of the function $y = x^2 - 7$ is:

$\text{Range} = \{y \mid y \geq -7\}$

In interval notation, this can be written as:

$\text{Range} = [-7, +\infty)$

This means that the function can take any value greater than or equal to -7, and there is no upper bound for the function's values.