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.

Responces:
A
B
C
D

Answer 1

To determine whether each relation is a function, we will check for the vertical line test (in the case of graphs) and the definition of a function (where each input corresponds to exactly one output).

**Relation A:**
- The pairs are: (4, 4), (5, 5), (5, 0), (7, 8), (10, 1).
- When x = 5, there are two different outputs (y = 5 and y = 0).
- Therefore, Relation A is **not a function**.

**Relation B:**
- This relation is described as a U-shaped curve with its vertex at (-4.2, 0).
- A vertical line drawn anywhere on the graph will intersect the curve at most once, indicating that for each x-value there is only one corresponding y-value.
- Therefore, Relation B is a **function**.

**Relation C:**
- The equation is \( y = 4x + 53 \).
- This is a linear equation, and for every x-value there is exactly one corresponding y-value.
- Therefore, Relation C is a **function**.

**Relation D:**
- The equation is \( y = 8x^2 \).
- This represents a parabola that opens upwards, and like the curve in Relation B, a vertical line will intersect the graph at most once for each x-value.
- Therefore, Relation D is a **function**.

### Summary:
- **Relation A:** Not a function
- **Relation B:** Function
- **Relation C:** Function
- **Relation D:** Function

Responses:
- A → Not a function
- B → Function
- C → Function
- D → Function