Answer:
Changing the sign of the constant "a" from positive to negative affects the domain and range of the function f(x) = a[x].
1. Domain: The domain of a function represents the set of all possible values of x for which the function is defined. In this case, the function f(x) = a[x] is defined for all real numbers x. Therefore, changing the sign of the constant "a" does not affect the domain of the function.
2. Range: The range of a function represents the set of all possible values that the function can output. For the function f(x) = a[x], the constant "a" affects the range of the function.
- When "a" is positive, the function f(x) = a[x] will output positive values for positive values of x and negative values for negative values of x. Therefore, the range will consist of all positive and negative real numbers.
- When "a" is negative, the function f(x) = a[x] will output negative values for positive values of x and positive values for negative values of x. Therefore, the range will consist of all negative and positive real numbers.
In summary, changing the sign of the constant "a" from positive to negative does not affect the domain of the function, but it does change the range of the function from all positive and negative real numbers to all negative and positive real numbers, respectively.
Step-by-step explanation:
