Question

What is the range of y=3cosx-1?

a) -4 ≤ x ≤ 4
b) -4 ≤ x ≤ 2
c) -3 ≤ x ≤ 3
d) -2 ≤ x ≤ 0

Answer 1

Answer: The correct option is (b)
`-4\leq y\leq 2.`

Step-by-step explanation: We are given to select the correct range of the following function

`y=3\cos x-1.`

We know that the range of the cosine function is from - 1 to 1.

That is,

`-1\leq \cos x\leq 1\\\\\Rightarrow -(1)* 3\leq 3* \cos x\leq 3* 1\\\\\Rightarrow -3\leq 3\cos x\leq 3\\\\\Rightarrow -3-1\leq 3\cos x-1\leq 3-1\\\\\Rightarrow -4\leq 3\cos x-1\leq 2\\\\\Rightarrow -4\leq y\leq 2.`

Thus, the range of the given function is
`-4\leq y\leq 2.`

Option (b) is CORRECT.

Answer 2

For this case we have the following equation:

`y = 3cosx-1`
We must find the maximum and minimum values of the equation to find the range.
We have then:
For x = 0

`y = 3cos (0) -1 y = 3 (1) -1 y = 3-1 y = 2`
For x = pi

`y = 3cos ( \pi ) -1 y = 3 (-1) -1 y = -3-1 y = -4`
The range of the function is given by:
[-4, 2]
Equivalently,
-4 ≤ x ≤ 2
Answer:
b) -4 ≤ x ≤ 2