Question

in a function, no input value has more than one ____. checking if each input has only one output in a data table helps determine if it is a __. a circle on a graph is an example of a ____.

Explanation:

First Blank:

Step1: Recall function definition

A function is a relation where each input (domain value) has exactly one output (range value). So in a function, no input value has more than one output.

Step1: Relate input - output to function

Checking if each input has only one output is the key to determining if a relation (like from a data table) is a function.

Step1: Analyze circle as a graph

A circle fails the vertical line test (a vertical line can intersect a circle at more than one point), so it is not a function. It is a relation (since it's a set of ordered pairs (x,y) satisfying \(x^{2}+y^{2}=r^{2}\)) but not a function.

Answer:

output

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