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What is the range of [tex]f(x) = \sin(x)[/tex]?

A. The set of all real numbers [tex]-2\pi \leq y \leq 2\pi[/tex]

B. The set of all real numbers [tex]-1 \leq y \leq 1[/tex]

C. The set of all real numbers [tex]0 \leq y \leq 2\pi[/tex]

D. The set of all real numbers



Answer :

GinnyAnswer
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]
Hi1315

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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