Math  /  Discrete

QuestionSet A Set B -2 7 -4 9 0 -1 Answer Attempt 2 out of 2 The mapping diagram above \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ a function since \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ in \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ where there \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

Studdy Solution

STEP 1

What is this asking? We need to determine if the given mapping diagram represents a function and explain why or why not. Watch out! Remember, a function must map each element in the domain to exactly one element in the codomain!

STEP 2

1. Review function definition
2. Examine the mapping diagram
3. Check function criteria
4. Make a conclusion

STEP 3

Alright, let's kick this off by refreshing our memory on what makes a function a function!
A function is like a special relationship between two sets.
It's got some rules that make it unique:
1. Every element in the first set (we call it the domain) must be mapped to something in the second set (the codomain).
2. Here's the kicker: each element in the domain can only be mapped to **one** element in the codomain.

It's like a one-way street, no U-turns allowed!

STEP 4

Now, let's take a good look at our mapping diagram.
We've got two sets here:
Set A (our domain): 2-2, 4-4, and 00 Set B (our codomain): 77, 99, and 1-1

STEP 5

Let's follow those arrows!
They're showing us how the elements are mapped: - 2-2 is mapped to 77 - 4-4 is mapped to both 99 and 1-1 - 00 is mapped to 1-1

STEP 6

Time to play detective and see if our mapping follows the function rules!
1. **First rule:** Is every element in Set A (our domain) mapped to something in Set B? **Yes!** Each number in Set A has at least one arrow pointing to Set B.
2. **Second rule:** Does each element in Set A map to exactly one element in Set B? **Uh-oh!** We've hit a snag.
Look at 4-4 in Set A.
It's got two arrows pointing to different elements in Set B (99 and 1-1).
That's a no-no for functions!

STEP 7

Based on our investigation, we can now make our conclusion.
The mapping diagram does not represent a function.
Why? Because 4-4 in Set A is mapped to more than one element in Set B, which violates our second rule of functions.

STEP 8

The mapping diagram above is **not** a function since there is an element in Set A where there are multiple outputs in Set B.

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