Question

Which of the following statements are true regarding functions?

Check all that apply.

A. The vertical line test may be used to determine whether a function is one-to-one.
B. A sequence is a function whose domain is the set of real numbers.
C. A function is a relation in which each value of the input variable is paired with exactly one value of the output variable.
D. The horizontal line test may be used to determine whether a function is one-to-one.

I know A is true, I'm not positive about B or C, and I know D is false.

Answer 1

C isnt always true
for example, when you plug one value into a quadratic for y, it may provide two solutions so C isnt always true

Answer 2

so it's just A and B? @CrashOnce

Answer 3

not sure about B though @ikram002p a little help please

Answer 4

A is not true

Answer 5

the vertical line test is to make sure its a function

we use the horizontal line test to see if its 1-1

Answer 6

the definition of one to one is that f(a)=f(b) imples a=b. If a line fails the horizontal line test then what that means there are at least 2 different x values mapping to the same y value.

Answer 7

i.e. f(a) = f(b) but a \(\ne\) b

Answer 8

so A) false, vert line test is to test well if its a function (more technically it is used to make sure a relation is well defined i.e. a=b implies f(a) = f(b))
B) false, the domain of a sequence is \(\mathbb{N}\) the set of natural numbers
C) false; surely f(x) = x^2 is a function and we have -2,2 both mapping to 4
D) true: the reason I explained.

Answer 9

it says that C is also correct... can I argue that?

Answer 10

I miss read C. But C still does not give the complete definition of a function.

C) False; A function is a relation that is well defined (this is what the option says) AND defined everywhere. This means for all x there is a y such that f(x) = y so

A) false, vert line test is to test if its a function (more technically it is used to make sure a relation is well defined i.e. a=b implies f(a) = f(b))
B) false, the domain of a sequence is N the set of natural numbers
C) edit above*
D) true: the reason I explained.