g(x)=3 sin x domain and range
is the domain: {xER}
range {yEr|3< or = y}?
domain is all real x
range is from y = -3 to y = +3
Note in this question and your last one that the range of the sine function is from -1 to +1 (same with cos or with sin (w t + phi) where phi is a constant phase angle)
therefore range of a sin w t or a cos w t is -a to + a
oh yeah, thanks
To determine the domain and range of the function g(x) = 3 sin x, we need to understand the properties of the sine function.
The domain of the sine function is all real numbers because there are no restrictions on the values of x for which the sine function is defined. Therefore, the domain of g(x) = 3 sin x is {x ∈ R} or in simpler terms, "all real numbers".
Next, we need to consider the range of the function g(x) = 3 sin x. The range of the sine function is typically between -1 and 1, inclusive. However, since g(x) is multiplied by 3, the range of g(x) is multiplied by 3 as well. This means the range of g(x) will be between -3 and 3, inclusive.
Therefore, the range of g(x) = 3 sin x is {y ∈ R | -3 ≤ y ≤ 3}, or in simpler terms, "all real numbers y where -3 is less than or equal to y, and y is less than or equal to 3".