Practice worksheet for determining whether relations are functions, featuring four different representations: a table, a graph, a mapping diagram, and a set of ordered pairs.

To determine whether each relation is a function, we need to check if each input (x-value) has exactly one output (y-value). If any input has more than one output, it’s not a function.

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Problem 1:
We have this table:

```
x | -1 0 3 4 -1
y | -2 0 -1 -1 4
```

Look at the x-values: -1 appears twice — once paired with y = -2 and again with y = 4.
That means the input -1 gives two different outputs.
→ So, this is NOT a function.

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Problem 2:
This is a graph that looks like a “V” shape (absolute value graph).
We use the vertical line test: if any vertical line crosses the graph more than once, it’s not a function.
In this case, no vertical line will cross the graph more than once — every x has only one y.
→ So, this IS a function.

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Problem 3:
This is a mapping diagram.
Left side (inputs): -2, -1, -2
Right side (outputs): 9, 1, 2

Notice: -2 maps to both 9 and 2.
That means one input (-2) has two different outputs.
→ So, this is NOT a function.

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Problem 4:
This is a set of ordered pairs:
{(-2, 1), (-3, 1), (-4, 1), (-5, 1)}

Check the x-values: -2, -3, -4, -5 — all are different.
Each x is paired with only one y (in this case, all pair with 1, but that’s fine — multiple inputs can share the same output).
→ So, this IS a function.

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Final Answer:
1. Not a function
2. Is a function
3. Not a function
4. Is a function