Question

Область значений функции у=3/х(дробь) -12

Answer 1

Решение задания приложено

Answer 2

На фотке, если это оно, глянь

Answer 3

To determine the range of the function $y = \frac{3}{x} - 12$, we need to find all possible values that the function can take for different values of $x$.

The function is defined as $y = \frac{3}{x} - 12$.

First, let's consider the domain of the function. The function is defined for all real numbers except $x = 0$ because division by zero is undefined. So, the domain of the function is $\mathbb{R}$ (all real numbers) except $x = 0$.

Next, let's analyze the behavior of the function as $x$ approaches positive infinity ($+\infty$) and negative infinity ($-\infty$).

As $x$ approaches positive infinity ($+\infty$), $\frac{3}{x}$ approaches 0, and the function becomes:

$\lim_{{x \to +\infty}} y = 0 - 12 = -12$.

As $x$ approaches negative infinity ($-\infty$), $\frac{3}{x}$ approaches 0 again, but this time, with a negative sign, and the function becomes:

$\lim_{{x \to -\infty}} y = 0 - 12 = -12$.

Therefore, the range of the function is all real numbers except for the value -12, as the function can take any value less than -12 or greater than -12, but it cannot reach the value -12. In interval notation, the range is $(-\infty, -12) \cup (-12, +\infty)$.