Question

Review the graph of y = sin(x). Based on the graph, what are the domain and range of the sine function? Y 3+ 2+ domain: [0, 2TT); range: [-1, 1] O domain: (-1, 1); range: [0, 2TT) domain: (-1, 1); range: (-0, 0) domain:(-0, 0); range: [-1, 1] I JT 57 Зл 4 Зл 7л 2 2 4 -1+ -2+ -3+​

Answer 1

Answer:

The right answer is domain: (-∞, ∞); range: [-1, 1] ⇒ D

Step-by-step explanation:

In any function,

Domain is the values of x

Range is the values of y corresponding to x

In the function y = sin(x),

∵ The graph ends with arrows

→ That means there is many cycle not 1 cycle

∴ x ∈ R

→ That means x can be any value from -∞ to ∞

∵ x is the domain of the function

∵ R is the set of real numbers

∴ Domain = {x : x ∈ R} = (-∞, ∞)

∵ sin($\frac{\pi}{2}$) = 1

∵ The greatest value of y is 1 at x = $\frac{\pi}{2}$

∵ sin($\frac{3\pi}{2}$) = -1

∵ The smallest value of y is -1 at x = $\frac{3\pi}{2}$

∴ -1 ≤ y ≤ 1

∵ y is the range of the function

∴ Range = {y : -1 ≤ y ≤ 1} = [-1, 1]

∴ The right answer is domain: (-∞, ∞); range: [-1, 1]