Domain Range

Question

4
1
3

2
4
1

Based on the mapping diagram of the relation, determine which of the given options is accurate. Option #1: The relation is a function. Option #2: The relation is not a function. (1 point)

Answer 1

To determine if the relation is a function, we need to check if each input (from the domain) is associated with exactly one output (from the range).

From the mapping diagram you provided:

• The number 4 in the domain maps to 1 in the range (4 → 1).
• The number 3 does not seem to have a mapping shown.
• The number 2 in the domain maps to 4 in the range (2 → 4).
• The number 1 in the domain does not seem to have a mapping shown.

Since we only have outputs for the inputs 4 and 2 (mapping to 1 and 4, respectively) and there are no repeating inputs mapping to different outputs, we can't assess the values of 3 and 1 properly due to their lack of specified mappings.

However, for it to be classified as a function, every element in the domain must map to one, and only one, element in the range. The information provided indicates:

• Input 4 maps to 1 (valid).
• Input 2 maps to 4 (valid).
• Inputs 3 and 1 do not have mappings, but since they do not have multiple outputs for any mapped input, we don't have any contradictions in the functions.

Therefore, since there are no instances where an input maps to multiple outputs, we can conclude:

Option #1: The relation is a function.

Answer 2

It's 4 and 3 to 1 and 2 and 1 to 4

Answer 3

Thank you for the clarification! Based on the new information:

1. 4 maps to 1
2. 3 maps to 1
3. 2 maps to 4
4. 1 maps to 4

Now we can analyze this properly.

In this relation:

• Both 4 and 3 map to 1.
• Both 2 and 1 map to 4.

Since we have multiple inputs (4 and 3) mapping to the same output (1) and multiple inputs (2 and 1) mapping to the same output (4), there are no input values that map to multiple outputs, which is acceptable in a function.

However, the main criterion for a relation to be a function is that each input must map to exactly one output. In this case, each unique input (4, 3, 2, 1) still maps to only one output.

Thus, the relation is indeed a function.

So again, the accurate option is:

Option #1: The relation is a function.