A function is defined as a relationship between two quantities where every input value has ______________.(1 point)
Responses
no value.
no value.
exactly one output value
exactly one output value
infinitely many values
infinitely many values
exactly one input value
exactly one output value
exactly one output value
The correct answer is "exactly one output value."
To understand why, let's look at the definition of a function. A function is a mathematical relationship between two sets of values, called the domain and the range. The domain represents all possible input values, while the range represents all possible output values.
In a function, every input value (or element in the domain) must have exactly one corresponding output value (or element in the range). This means that for each input, there is only one output associated with it.
To determine if a given relationship is a function or not, we can use the vertical line test. If a vertical line intersects the graph of the relationship at more than one point, then it is not a function because one input value would have multiple output values. However, if every vertical line intersects the graph at most one point, then it is a function. This corresponds to the idea that every input value has exactly one output value.
Therefore, in a function, every input value has exactly one output value.