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+
1 answer:
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() = 1
∵ The greatest value of y is 1 at x =
∵ sin() = -1
∵ The smallest value of y is -1 at x =
∴ -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]
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