Mapping Diagrams worksheet - Free Printable

Let’s solve each mapping diagram one by one. We’ll plug in each domain value into the equation to find the range value, then see what kind of relation it is.

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1. y = 2x + 1

Domain values: -3, -2, -1, 0, 1, 2, 3

Calculate y for each:

- x = -3 → y = 2(-3) + 1 = -6 + 1 = -5
- x = -2 → y = 2(-2) + 1 = -4 + 1 = -3
- x = -1 → y = 2(-1) + 1 = -2 + 1 = -1
- x = 0 → y = 2(0) + 1 = 0 + 1 = 1
- x = 1 → y = 2(1) + 1 = 2 + 1 = 3
- x = 2 → y = 2(2) + 1 = 4 + 1 = 5
- x = 3 → y = 2(3) + 1 = 6 + 1 = 7

Each x gives a different y. No repeats in range from different x’s.

→ Relation is: one to one

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2. y = 3x

Domain values: -3, -2, -1, 0, 1, 2, 3

Calculate y:

- x = -3 → y = 3(-3) = -9
- x = -2 → y = 3(-2) = -6
- x = -1 → y = 3(-1) = -3
- x = 0 → y = 3(0) = 0
- x = 1 → y = 3(1) = 3
- x = 2 → y = 3(2) = 6
- x = 3 → y = 3(3) = 9

Again, every x gives a unique y. No two x’s give same y.

→ Relation is: one to one

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3. y = x²

Domain values: -3, -2, -1, 0, 1, 2, 3

Calculate y:

- x = -3 → y = (-3)² = 9
- x = -2 → y = (-2)² = 4
- x = -1 → y = (-1)² = 1
- x = 0 → y = (0)² = 0
- x = 1 → y = (1)² = 1
- x = 2 → y = (2)² = 4
- x = 3 → y = (3)² = 9

Notice:
- x = -1 and x = 1 both give y = 1
- x = -2 and x = 2 both give y = 4
- x = -3 and x = 3 both give y = 9

So multiple x’s map to same y → that’s “many to one”

But also, each x maps to only one y (no x goes to two y’s), so not “one to many” or “many to many”.

→ Relation is: many to one

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4. y = x – 2

Here, the RANGE is given: 2, 4, 6, 8, 10

We need to find which DOMAIN values produce these.

Since y = x – 2, then x = y + 2

So:

- If y = 2 → x = 2 + 2 = 4
- If y = 4 → x = 4 + 2 = 6
- If y = 6 → x = 6 + 2 = 8
- If y = 8 → x = 8 + 2 = 10
- If y = 10 → x = 10 + 2 = 12

So domain values are: 4, 6, 8, 10, 12

Each x gives one y, and each y comes from only one x.

→ Relation is: one to one

Wait — but look at the diagram: arrows go FROM domain TO range. In this case, the range is fixed, and we’re finding domain? Actually, no — the problem says “complete the mapping diagrams”. The left oval is DOMAIN, right is RANGE. Arrows go from domain to range.

In #4, the RANGE has numbers: 2, 4, 6, 8, 10 — and arrows point TO them. So we must figure out what DOMAIN values would produce those outputs using y = x – 2.

That means: if output (y) is 2, input (x) must be 4 → so arrow from 4 to 2.

Similarly:

- 6 → 4
- 8 → 6
- 10 → 8
- 12 → 10

So domain should be: 4, 6, 8, 10, 12

And each domain value maps to exactly one range value, and no two domain values map to same range value.

Still → one to one

BUT — wait! Look again at the diagram for #4. It shows FIVE arrows going to five range values. That suggests there are five domain values. And since each domain value produces a unique range value (because it's linear with slope 1), it’s still one-to-one.

However — let me double-check: could it be that they want us to assume domain is something else? No — the rule is y = x – 2. To get range values 2,4,6,8,10, you MUST have domain 4,6,8,10,12. Each x → one y, each y ← one x.

So yes — one to one.

But hold on — maybe I misread. Let me check the original image description again.

Actually, in the user’s image, for #4, the DOMAIN oval is empty, and RANGE has 2,4,6,8,10 with arrows pointing to them. So we fill in the domain as above.

Final decision: still one to one.

Wait — another thought: sometimes “many to one” means multiple inputs to same output. Here, no — each input gives unique output.

Yes.

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Now, let’s write final answers clearly.

Final Answer:

1. Relation is: one to one
2. Relation is: one to one
3. Relation is: many to one
4. Relation is: one to one