Question

Область значение функции y=2cosx-4

Answer 1

Ответ:

Объяснение:   надо знать -1≤ cosx≤ 1

тогда    * на 2         -2  ≤ 2cosx≤2

   отнимем 4         -6≤ 2cosx-4≤-2

Answer 2

To find the range (or the set of all possible values) of the function $y = 2\cos(x) - 4$, we need to consider the range of the cosine function and then adjust it based on the coefficient and constant term.

The cosine function $\cos(x)$ has a range of $[-1, 1]$, meaning it can take values between -1 and 1 inclusive.

Now, let's see how the function $y = 2\cos(x) - 4$ affects the range:

1. The coefficient of 2 before $\cos(x)$ means that the amplitude of the cosine function is doubled. Since the amplitude of $\cos(x)$ is 1, after multiplying by 2, the amplitude becomes 2.

2. The constant term of -4 means that the entire graph of the cosine function is shifted downward by 4 units.

Combining these adjustments, the range of the function $y = 2\cos(x) - 4$ will be:

$y \in [-2 - 4, 2 - 4] = [-6, -2]$

So, the range of the function $y = 2\cos(x) - 4$ is $[-6, -2]$. This means that the function can take any value between -6 and -2, inclusive.