A company manufactures fence sections for residential use. The number, s, of sections that can be produced per day is related to the number of hours, h, of labour required by the function s=2.1 square root h (Show your work)
a) State the domain and range for the function. (2 marks)
To find the domain and range of the function s = 2.1 √h, we need to consider the possible values for the variable h.
The square root of a number is only defined for non-negative values, so h must be greater than or equal to 0 to ensure the function is valid.
Therefore, the domain of the function is h ≥ 0.
To find the range, we can consider the possible values for s. Since the square root of any non-negative number is always non-negative, s will also be non-negative.
Therefore, the range of the function is s ≥ 0.
To find the domain and range of the function s = 2.1√h, let's analyze each one individually.
Domain:
The domain refers to all possible values that the input variable, in this case, 'h,' can take. Since the number of hours of labor can never be negative (since time cannot be negative), the domain will be all non-negative real numbers.
Therefore, the domain for this function is h ≥ 0.
Range:
The range refers to all possible values that the output variable, in this case, 's' (number of fence sections), can take. To determine the range, we need to consider the restrictions and characteristics of the function.
Since we have an expression with the square root (√h), we know that the value inside the square root must be non-negative, as the square root of a negative number is undefined in the real number system.
So, the range of this function is all non-negative real numbers.
Therefore, the range for this function is s ≥ 0.
In summary:
Domain: h ≥ 0
Range: s ≥ 0