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!
1 answer