a function is defined as a relationship between two quantities where every input has _______.
exactly one input value
no value
exactly one output value
infinitely many values
exactly one output value
A function is defined as a relationship between two quantities where every input has exactly one output value.
A function is defined as a relationship between two quantities where every input has exactly one output value. In other words, for each input value, there is only one corresponding output value. So the correct completion of the sentence would be "exactly one output value."
To understand this concept, let's take an example. Consider a simple function where the input represents the age of a person, and the output represents their height. If you have a function that maps age to height, each age will correspond to one specific height. For instance, if the input (age) is 20, the output (height) may be 170 cm. There won't be multiple possible heights for the same age in a well-defined function.
In contrast, if a function has more than one output value for a given input, it is not considered a function. This would violate the rule of having exactly one output value for each input, and we would call it a relation instead.
So, to summarize, a function ensures that each input value has exactly one output value, providing a well-defined and predictable relationship between the two quantities.