Question

Four relations are shown.

Relation A has two columns x and y. When x is 4, y is 4. When x is 5, y is 5. When x is 5, y is 0. When x is 7, y is 8. When x is 10, y is 1. Relation B has a coordinate plane with a U-shaped curve open to the right with its vertex at (-4.2, 0). Relation C shows the equation 4x plus 53 equals to y. Relation D shows the equation y equal to 8x exponential 2.

Drag the name of each relation to identify whether the relation is a function or not a function.
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Answer 1

Let's analyze each relation to determine if they are functions:

1. **Relation A**: This relation has two columns (x, y). To be a function, each input (x) must map to exactly one output (y).
- When x is 4, y is 4 → valid
- When x is 5, there are two outputs (y = 5 and y = 0) → not valid
- When x is 7, y is 8 → valid
- When x is 10, y is 1 → valid
Since there are multiple outputs (y values) for the same input (x = 5), **Relation A is not a function**.

2. **Relation B**: This relation shows a U-shaped curve (which means it could represent a quadratic function) open to the right with its vertex at (-4.2, 0).
- This relation can be expressed in the form of a function, where any x-value has a unique corresponding y-value. Therefore, **Relation B is a function**.

3. **Relation C**: The equation given is \( 4x + 53 = y \), which can be rearranged to \( y = 4x + 53\).
- This is a linear equation and each input (x) will map to exactly one output (y). Therefore, **Relation C is a function**.

4. **Relation D**: The equation given is \( y = 8x^2 \), which describes a quadratic function.
- Similar to Relation B, for each x-value, there is a unique y-value, meaning it satisfies the definition of a function. Thus, **Relation D is also a function**.

In summary:
- **Relation A**: Not a function
- **Relation B**: Function
- **Relation C**: Function
- **Relation D**: Function