Final answer:
The set of ordered pairs is not a function because one input maps to two different outputs. However, the quadratic equation y = -4x² + 45x + 9 is a function because each input has a single output.
Step-by-step explanation:
To determine which of the given options are functions, we need to apply the definition of a function. A function is a relation in which each input (often denoted as x) has exactly one output (often denoted as y). Let's assess each option:
- {(-4, 2), (-2, 1), (-1, 3), (-1, 4), (0, 5), (2, 5)}: This is not a function because the input -1 corresponds to two different outputs (3 and 4).
- y = -4x² + 45x + 9: This is a function because for each value of x there is exactly one corresponding value of y. This is a quadratic equation, and quadratic equations are always functions as they pass the vertical line test.
Therefore, the only option that is a function is the quadratic equation y = -4x² + 45x + 9.