Which of the following statements are true regarding functions? check all that apply. a. the horizontal line test may be used to determine whether a function is one-to-one. b. a function is a relation in which multiple values of the input variable are paired with at least one of the output variable. c. the vertical line test may be used to determine whether a relation is a function. d. a sequence is a function whose domain is the set of rational numbers.

The horizontal line test is used to determine if a function is one-to-one.
It works by testing if a horizontal line intersects the graph of a function once or more than once.
If the horizontal line intersects the function's graph more than one time, that means the function is not one-to-one.
This means answer choice A is true.

In a function, every input must be paired with exactly one output.
If a single number appears more than once, both as input values, the relation is not a function.
This means answer choice B is incorrect.

The vertical line test is used to determine whether or not a curve in a graph represents a function or not.
This works by checking if any inputs, x-values, are paired with multiple outputs, y-values, by drawing a vertical line through points on the curve.
This means answer choice C is true.

A sequence is a data set, or just set of numbers, that follow a specific pattern.
This could be by a common difference or common ratio.
Sometimes sequences are defined as functions with a domain of natural numbers.
Natural numbers are whole positive numbers.
Rational numbers are are numbers that can be written as a simple fraction.
Rational numbers can be decimals, fractions, and even negative.
While answer choice D is close to being true, the domain of sequences is always natural, numbers, not rational.
This means answer choice D is incorrect.

Answers:
A. The horizontal line test may be used to determine whether a function is one-to-one
C. The vertical line test may be used to determine whether a relation is a function.

Hope this helps!