Answer:
In the equation p(12.5) = -8(12.5) + 100, "p" represents a function, and you are evaluating this function at a specific input value, which is 12.5. The equation calculates the output or value of the function at that specific input.
Domain: The domain of a function represents all the possible input values (or values of the independent variable) for which the function is defined or meaningful. In this case, since the equation is a simple linear equation, it is defined for all real numbers. Therefore, the reasonable domain for this function is the set of all real numbers, often denoted as (-∞, ∞).
Range: The range of a function represents all the possible output values (or values of the dependent variable) that the function can produce for the given domain. In this case, the function is a linear function, and the range is determined by the slope and intercept of the line.
The equation p(12.5) = -8(12.5) + 100 calculates the value of p at 12.5. When you evaluate it, you get p(12.5) = -100 + 100 = 0.
This means that when the input value is 12.5, the output value (p) is 0. So, for this specific function, the reasonable range is the set containing only the value 0.
To summarize:
The reasonable domain is all real numbers (-∞, ∞).
The reasonable range is the single value {0} since the function produces an output of 0 when the input is 12.5.