Which of the following statements defines a function? Choose the correct answer below. A. A function is a set of ordered pairs
in which none of the first components in the ordered pairs are negative. B. A function is a set of ordered pairs where all the first components in the ordered pairs have the same value. C. A function is a set of ordered pairs in which each second component in the ordered pairs corresponds to exactly one first component. D. A function is a set of ordered pairs in which each first component in the ordered pairs corresponds to exactly one second component.
Answer: D. A function is defined as a collection of ordered pairs where each first component corresponds to exactly one second component in the pairs.
Step-by-step explanation: In mathematics, a Function refers to a relationship between two sets, in which every element from the first set matches with elements from the second set just once. This relationship demonstrates how one quantity relies on another, like how distance is related to time traveled.
<pA function signifies a process where each element (x) from set X is associated with one unique element in set Y or f(x). The set X represents the domain while set Y or f(x) constitutes the codomain.
Each value of x acts as the function's input or variable and each corresponding y represents the function's value or image of x by f.
The correct choice is D. For any value x within the domain of your function, it is crucial that there is ONLY ONE corresponding value of y. If you encounter more than one y linked to a single x, that relationship does not qualify as a function.
