Question

what is the range of this function? the trigonometric functions intercept the x-axis at minus 2 pi, minus pi, 0, pi, 2 pi, and pass parallel to the y-axis. the dotted lines intercept the x-axis at every pi by 2 units. a. all real numbers where b. c. all real numbers where d.

Answer 1

The range of the described sine function, which oscillates between +1 and -1 and passes parallel to the y-axis, is [-1, 1]. This interval represents the set of all possible output values of the function based on its described behavior.

Step-by-step explanation:

The range of a function describes the set of possible output values. For a sine function, as described in the question, which oscillates between +1 and -1 at intervals of π (pi) along the x-axis and passes parallel to the y-axis, the range is the interval to which the function's values are limited. The given description matches the characteristics of a sine wave, which is a periodic function and has a range between its maximum and minimum values that it reaches regularly.

Since a sine function oscillates between +1 and -1, the range of this function would be [-1, 1]. This means the highest value the function reaches is +1 and the lowest is -1. There is no need to know where the dotted lines that intersect the x-axis at every π/2 units fall, as they seem to refer to an aspect of the question that isn't related to determining the range.