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

 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

Answer 2

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,

$-1\leq \cos x\leq 1\\\\\Rightarrow -(1)\times 3\leq 3\times \cos x\leq 3\times 1\\\\\Rightarrow -3\leq 3\cos x\leq 3\\\\\Rightarrow -3-1\leq 3\cos x-1\leq 3-1\\\\\Rightarrow -4\leq 3\cos x-1\leq 2\\\\\Rightarrow -4\leq y\leq 2.$

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

Option (b) is CORRECT.