Final answer:
The equation y = -3x^2 + 4x - 11 represents both a relation and a function because it assigns exactly one output of y for each input of x, and is also a set of ordered pairs. It is a quadratic equation, not linear, because of the x-squared term.
Step-by-step explanation:
The equation y = -3x^2 + 4x - 11 represents both a relation and a function. In mathematics, a function is defined as a relation where each element in the domain (the set of all possible values of x) is associated with exactly one element in the codomain (the set of all possible values of y). Given that for every value of x there is only one corresponding value of y in this equation, it qualifies as a function. It is also a relation since a relation is any set of ordered pairs, and the equation can be used to produce a set of ordered pairs (x, y).
Additionally, the equation y = -3x^2 + 4x - 11 is not linear. It is a quadratic equation because of the x-squared term (-3x^2). This means it will graph out to a parabola, not a straight line. Based on the coefficients, the parabola opens downward (since the coefficient of x^2 is negative) and its graph will vary based on the values of x.