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Sagot :
To determine the range of the function [tex]\( f(x) = \sin(x) \)[/tex], let's first understand what the range of a function represents. The range of a function is the set of all possible output values (y-values) that the function can produce.
The sine function, [tex]\( \sin(x) \)[/tex], is a periodic function that oscillates between a maximum value and a minimum value. To find these values, consider the general properties of the sine function:
- The sine function has a maximum value of 1.
- The sine function has a minimum value of -1.
These characteristics imply that the sine function will output values that are contained within and including these bounds.
Therefore, the range of the function [tex]\( f(x) = \sin(x) \)[/tex] is the set of all real numbers [tex]\( y \)[/tex] such that [tex]\( -1 \leq y \leq 1 \)[/tex].
Given the options:
- The set of all real numbers [tex]\( -2\pi \leq y \leq 2\pi \)[/tex]
- The set of all real numbers [tex]\( -1 \leq y \leq 1 \)[/tex]
- The set of all real numbers [tex]\( 0 \leq y \leq 2\pi \)[/tex]
- The set of all real numbers
The correct answer is:
The set of all real numbers [tex]\( -1 \leq y \leq 1 \)[/tex]
The sine function, [tex]\( \sin(x) \)[/tex], is a periodic function that oscillates between a maximum value and a minimum value. To find these values, consider the general properties of the sine function:
- The sine function has a maximum value of 1.
- The sine function has a minimum value of -1.
These characteristics imply that the sine function will output values that are contained within and including these bounds.
Therefore, the range of the function [tex]\( f(x) = \sin(x) \)[/tex] is the set of all real numbers [tex]\( y \)[/tex] such that [tex]\( -1 \leq y \leq 1 \)[/tex].
Given the options:
- The set of all real numbers [tex]\( -2\pi \leq y \leq 2\pi \)[/tex]
- The set of all real numbers [tex]\( -1 \leq y \leq 1 \)[/tex]
- The set of all real numbers [tex]\( 0 \leq y \leq 2\pi \)[/tex]
- The set of all real numbers
The correct answer is:
The set of all real numbers [tex]\( -1 \leq y \leq 1 \)[/tex]
Answer:
B
Step-by-step explanation:
The function f(x) = sin(x) is a trigonometric function whose range is determined by the values that the sine function can take.
The sine function oscillates between -1 and 1 for all real numbers x.
Therefore, the correct answer is:
B. The set of all real numbers [tex]\(-1 \leq y \leq 1\)[/tex]
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