Question

Match the functions with their ranges. Tiles y = 3sin(x − π) (-∞, ∞) y = 1 − sin(x) [-1, 7] y = 3 + 4cos(x − π) [-3, 3] y = 2 + cot(x) [0, 2] Pairs

Answer 1

We will evaluate all functions for two values of the domain and thus find the range:

 For y = 3sin (x - π):
 When x = (3/2) π we have:
 y = 3sin ((3/2) π - π)
 y = 3sin ((1/2) π)
 y = 3 (1)
 y = 3
 When x = (5/2) π we have:
 y = 3sin ((5/2) π - π)
 y = 3sin ((3/2) π)
 y = 3 (-1)
 y = -3
 Therefore, the range of this function is:
 [-3, 3]

 For y = 3 + 4cos (x - π)
 When x = 0 we have:
 y = 3 + 4cos (0 - π)
 y = 3 + 4 (-1)
 y = 3 - 4
 y = -1
 When x = π we have:
 y = 3 + 4cos (π - π)
 y = 3 + 4 (1)
 y = 3 + 4
 y = 7
 Therefore, the range of this function is:
 [-1, 7]

 For y = 2 + cot (x):
 This function can take any value of y.
 Therefore, the range of the function is:
 (-∞, ∞)