which of the following statements is not true?\nchoose the correct answer.\na. every function that passes…

which of the following statements is not true?\nchoose the correct answer.\na. every function that passes the vertical line test is one - to - one.\nb. a function f is one - to - one if for any two range values f(u) and f(v), f(u)=f(v) implies that u = v.\nc. a function f is one - to - one if for any values a≠b in the domain of f, f(a)≠f(b).\nd. every function that passes the horizontal line test is one - to - one.

which of the following statements is not true?\nchoose the correct answer.\na. every function that passes the vertical line test is one - to - one.\nb. a function f is one - to - one if for any two range values f(u) and f(v), f(u)=f(v) implies that u = v.\nc. a function f is one - to - one if for any values a≠b in the domain of f, f(a)≠f(b).\nd. every function that passes the horizontal line test is one - to - one.

Answer

Brief Explanations:

  • Option A:
    • The vertical line test is used to determine if a relation is a function. A function passes the vertical line test if for every (x)-value there is exactly one (y)-value. But a function like (y = x^{2}) passes the vertical line test (it is a function) but is not one - to - one (since (f(2)=f(- 2)=4)).
  • Option B:
    • By the definition of a one - to - one function, if (f(u)=f(v)) implies (u = v) for (u) and (v) in the domain of (f), then (f) is one - to - one.
  • Option C:
    • If (a\neq b) in the domain of (f) and (f(a)\neq f(b)), this is another way of stating the one - to - one property. If different inputs give different outputs, the function is one - to - one.
  • Option D:
    • The horizontal line test: A function (y = f(x)) is one - to - one if and only if every horizontal line intersects the graph of the function at most once. So, if a function passes the horizontal line test, it is one - to - one.

Answer:

A. Every function that passes the vertical line test is one - to - one.