Question

1. select all descriptions that accurately define the meaning of a function.

a. every x-coordinate has one unique y-coordinate.
b. every y-coordinate has one unique x-coordinate.
c. every dependent variable has one unique independent variable.
d. every independent variable has one unique dependent variable.
e. set of ordered pairs.

Explanation:

• A function is defined such that each input (independent variable/x-coordinate) maps to exactly one output (dependent variable/y-coordinate).
• Option a matches this: each x-coordinate has one unique y-coordinate.
• Option d restates this using variable terms: each independent variable has one unique dependent variable.
• Option e is also correct, as a function can be formally represented as a set of ordered pairs where no two pairs share the same first element.
• Options b and c are incorrect because a function can have multiple inputs mapping to the same output, so y-coordinates/dependent variables do not need unique x-coordinates/independent variables.

Answer:

a. Every x-coordinate has one unique y-coordinate.
d. Every independent variable has one unique dependent variable.
e. Set of ordered pairs.