Question

Match the functions with their ranges. Thanks

Answer 1

y=3sin(x-pi), range=[-3,3]
y=1-sinx, range=[0,2]
y=3+4cos(x-pi), range=[-1,7]
y=2+cotx, range=(-inf,inf)

Answer 2

Functions Range

y = 3sin(x - π ) : [-3, 3]

y = 1 - sin(x) : [0, 2]

y = 3 + 4cos(x - π) : [-1, 7]

y = 2 + cot(x) : (-∞, ∞)

Explanation:

The Range is the output values of the function.

The range of sin(x) and cos(x) function is [-1, 1]

The range of tan(x) and cot(x) function is (-∞, ∞).

The range of cosec(x) and sec(x) function is (-∞ , -1] U [1 , + ∞).

1. y = 3sin(x - π ) Here range of y is 3 times of [-1, 1]

Hence, Range of y = [-3, 3]

2. y = 1 - sin(x) = 1 - [-1, 1] = [0, 2]

Hence, Range of y = [0, 2]

3. y = 3 + 4cos(x - π) Here range of y is 4 times of [-1, 1] + 3

⇒ 4 × -1 + 3 = -1 and 4 × 1 + 3 = 7

Hence, Range of y is [-1, 7].

4. y = 2 + cot(x) Since, range of cot(x) = (-∞, ∞)

so, adding any number in (-∞, ∞) is also (-∞, ∞).

Hence, Range of y is (-∞, ∞).