Which of the following statements are true regarding functions?

A function is a relation in which multiple values of the input variable are paired with at least one of the output variable.

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

The vertical line test may be used to determine whether a relation is a function.

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

Question

Which of the following statements are true regarding functions?

A function is a relation in which multiple values of the input variable are paired with at least one of the output variable.

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

The vertical line test may be used to determine whether a relation is a function.

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

debbieg · Answer

Definitely NOT the first one. to be a function, it is certainly not necessary that "multiple" values of the input are paired with 1 (or more) values of the output. All that is REQUIRED in order for a relation to be a function is that each input is paired with NO MORE THAN 1 output value. ("if you know x, you know y.") This is what is tested by the vertical line test, since IF it does not hold (and an x is paired to 2 or more y's) then at that value of x, a vertical line will intersect the graph of the relation twice.

Also, if it is the case that each output value is paired with EXACTLY ONE input value (e.g., "if you know y, you know x"), then the function is one-to-one (and invertible). The horizontal line test is the counterpart to the vertical line test in this regard. IF it does not hold (and a y is paired to 2 or more x's) then at that value of y, a horizontal line will intersect the graph of the relation twice.

john_es · Answer

Agree with @DebbieG, it is a sufficient condition but not necessary.

anonymous · Answer

so it's a and c?

debbieg · Answer

It is NOT a. As I said above.

C is true - do you see why? 

And one other.... read again what I wrote.

john_es · Answer

It's true, there is another one.

debbieg · Answer

Understanding C and D are really about understanding the vertical line test and the horizontal line test, respectively. If you understand what they are, how they work, why they work, then you will know what to say about C and D. :)

anonymous · Answer

Oh I see now, if the horizantal test fails it won't be one-to-one

debbieg · Answer

Exactly - think of f(x)=x^2. Fails the horizontal line test, and not OTO since, for example:

f(2)=f(-2)=4

It is NOT true that "If you know y, you know x"

anonymous · Answer

so C and D are true answers