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.

Answer 1

Based on the information provided about the four relations, let's analyze each one:

### Relation A
The relation can be summarized as follows based on the given points:

- (4, 4)
- (5, 5)
- (5, 0) (Note: This point indicates that for x = 5, there are two different y-values, which suggests this is not a function.)
- (7, 8)
- (10, 1)

**Analysis**:
- Since the point (5, 5) and (5, 0) both correspond to the same x-value (5) but different y-values, Relation A does not define a function.

### Relation B
This relation describes a U-shaped curve that opens to the right with its vertex at (-4.2, 0).

**Analysis**:
- This generally indicates a parabolic relation, likely described by an equation of the form \( y = a(x + 4.2)^2 \) where \( a > 0 \). The relation can take on multiple y-values for the same x-value depending on its shape.

### Relation C
This relation is described by the equation:

\[ y = 4x + 53 \]

**Analysis**:
- This is a linear equation, with a slope of 4 and a y-intercept at (0, 53). It defines a function since each x-value maps to exactly one y-value.

### Relation D
This relation is expressed as:

\[ y = 8x^2 \]

**Analysis**:
- This is a quadratic function that opens upwards. Like Relation C, it also defines a function since each x-value maps to exactly one y-value (specifically, y-values are always non-negative).

### Summary of Relations:
- **Relation A**: Not a function due to the same x-value having different y-values.
- **Relation B**: Likely not a function as it is a curve that can produce the same y for multiple x-values.
- **Relation C**: A function (linear).
- **Relation D**: A function (quadratic).

If you have any specific questions about these relations or need further analysis, feel free to ask!