Question

Which of the following statements are not true regarding functions?

A) the horizontal line test may be used to determine whether a function is one to one

B) the vertical line test may be used to determine whether a function is one to one

C) a function is a relation in which each value of the input variable is paired with at least one value of the output variable

D) a sequence is a function whose domain is the set of natural numbers

Answer 1

the answer that I got was A. because there is no such thing as a horizontal line test only vertical. hope this helped let me know if it is correct.

Answer 2

A.The horizontal line test may be used to determine whether a function is one to one.

C.a function is a relation in which value of input variable is paired with at least one value of output variable .

Explanation:

A. The horizontal line test may be used to determine whether a function is one to one .

This statement is false about regarding function because , the vertical line test used in place of horizontal line test .

When function is one to one it means each value of input variable paired with each different value of output variable.

B. The vertical line test may used to determine whether a function is one to one.

This statement is true. Because when a vertical line passing through the codomain of function then it intersect the graph of function atmost one point then we say function is one to one .

C. A function is a relation in which each value of input variable is paired atleast one value of output variable.

This statement is false . Because a function is a relation in which an element of domain can have only one value of image . An element of domain cannot have more than one value of image.

D. A sequence is a function whose domain is the set of natural numbers.

Yes, this statement is true about function .Because a sequence is a function in which domain is the set of natural numbers and range can be any subset of real numbers .