Find domain and range of 11-7 sin x
please help me to identifying domain and range
To find the domain and range of the function 11-7*sin(x), we need to consider the limitations of the sine function.
The domain represents all possible x-values for which the function is defined. Since the sine function is defined for all real numbers, there are no restrictions on the domain. Therefore, the domain of 11-7*sin(x) is (-∞, ∞), which means it is defined for all real numbers.
The range, on the other hand, represents all possible y-values or outputs of the function. The range of the sine function is bounded between -1 and 1. By multiplying sin(x) by -7 and then adding 11, we shift and scale the range. The lowest value the expression can reach is 11 - 7 = 4, and the highest value it can reach is 11 + 7 = 18.
Therefore, the range of the function 11-7*sin(x) is [4, 18]. It includes all real numbers between 4 and 18, including both endpoints.
Domain = R (R represents set of all Real numbers)
For range,
-1 <= sinx <= 1
Multiplying by -7
7 >= -7sinx >= -7
Adding 11
11+7 >= 11 - 7sinx >= 11-7
18 >= 11-7sinx >= 4
Range = [4,18]
domain is all reals
range of sinx is [-1,1]
range of 7sinx is thus [-7,7]
range of 11-7sinx is [4,18]