Question

a. how can an arrow diagram help to determine whether a relation is a function?
b. make an arrow diagram that describes the relation (3,39), (6,39), (9,78), (15,117).
a. choose the correct answer below.
a. if each input has one arrow that points to exactly one output, then the relation is a function. otherwise, the relation is not a function.
b. if each output has one arrow that points to exactly one input, then the relation is a function. otherwise, the relation is not a function.
c. if each output has one or more arrows that each point to more than one input, then the relation is a function. otherwise, the relation is not a function.
d. if each input has one or more arrows that point to outputs, then the relation is a function. otherwise, the relation is not a function.

Explanation:

To determine if a relation is a function, we use the definition: a function is a relation where each input (domain value) has exactly one output (range value). Let's analyze each option:

• Option A: States "If each input has one arrow that points to exactly one output, then the relation is a function. Otherwise, the relation is not a function." This matches the function definition (each input maps to exactly one output).
• Option B: Talks about outputs having one arrow to inputs, which is not the function definition (function focuses on inputs to outputs, not outputs to inputs).
• Option C: Says if outputs have arrows to multiple inputs, it's a function, which is incorrect (function requires inputs to have unique outputs, not outputs to have unique inputs).
• Option D: States if each input has one or more arrows to outputs, it's a function, which is wrong (a function requires each input to have exactly one output, not one or more).

Answer:

A. If each input has one arrow that points to exactly one output, then the relation is a function. Otherwise, the relation is not a function.