To determine which statement is true about the equation [tex]\( y = -3x^2 + 4x - 11 \)[/tex], let’s analyze whether it represents a relation, a function, or both.
### Step-by-step Analysis:
1. Identifying the Type of Equation:
- The equation [tex]\( y = -3x^2 + 4x - 11 \)[/tex] is a polynomial equation of degree 2 (quadratic equation).
2. Definition of a Relation:
- A relation in mathematics is a set of ordered pairs [tex]\((x, y)\)[/tex], where x is an element from the domain (input values), and y is an element from the range (output values).
- This quadratic equation describes a relationship between x and y, meaning for each value of x, there is a corresponding value of y. Thus, it is indeed a relation.
3. Definition of a Function:
- A function is a special type of relation where each input x corresponds to exactly one output y.
- For [tex]\( y = -3x^2 + 4x - 11 \)[/tex], if we choose any value of x, this equation will yield exactly one unique value of y. Therefore, each x-value maps to precisely one y-value, fulfilling the condition for being a function.
### Conclusion:
Since [tex]\( y = -3x^2 + 4x - 11 \)[/tex] both relates input x to output y (relation) and guarantees one unique y for each x (function), we can conclude that it represents both a relation and a function.
### Answer:
A. It represents both a relation and a function.
