2. Which of the following describe(s) f(x) = 0?
I. A zero function.
II. An identity function.
III. A constant function.
I and III
f(x) = 0 is described as a constant function.
Explanation:
A zero function is a function where the output is always zero, regardless of the input. In this case, f(x) = 0 is a zero function because it always evaluates to zero.
An identity function is a function where the output is equal to the input. In this case, f(x) = 0 is not an identity function because the output is always zero, not equal to the input.
A constant function is a function where the output is a fixed value that does not depend on the input. In this case, f(x) = 0 is a constant function because the output is always zero, regardless of the input.
To determine which of the following options describe the function f(x) = 0, let's consider each option:
I. A zero function: A zero function is a function that outputs zero for all inputs. In this case, f(x) = 0 does satisfy this condition since the function output is constantly zero regardless of the input value. Therefore, option I describes f(x) = 0.
II. An identity function: An identity function is a function where the output is equal to the input. In this case, f(x) = 0 does not satisfy this condition since the output is always zero, regardless of the input value. Therefore, option II does not describe f(x) = 0.
III. A constant function: A constant function is a function where the output is the same constant value for all inputs. In this case, f(x) = 0 does satisfy this condition since the function output is constantly zero for all input values. Therefore, option III describes f(x) = 0.
In conclusion, options I and III describe the function f(x) = 0, so the correct answer is I and III.