Think you’ve got your head wrapped around **Points, Vectors, and Functions**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

Q. Which of the following statements is true?

The equation *x*^{2} = y^{2} describes *y* as a function of *x*.

The equation *y*^{2} = x^{2} describes *x* as a function of *y*.

The equation *y = x*^{2} describes *y* as a function of *x*.

The equation *x*^{2} = y describes *x* as a function of *y*.

Q. We say *y = **f*(*x*) is a function of *x* if

there is only one possible *y* for each *x*.

there is only one possible *x* for each *y*.

both (A) and (B) hold.

none of the above.

Q. Which of the following functions is bounded above but not bounded below?

Q. We say a function *f*(*x*) defined on the whole real line is bounded below if

There is a real number *K* such that *f*(*x*) ≤ K for all real *x*.

There is a real number *x* such that *f*(*x*) ≤ K for all real *K*.

There is a real number *K* such that *f*(*x*) ≥ K for all real *x*.

There is a real number *x* such that *f*(*x*) ≥ K for all real *K*.

Q. Which of the following statements is FALSE?

If a function is strictly increasing, that function must also be non-decreasing.

If a function is non-decreasing, that function must also be strictly increasing.

It is possible for a function to be both non-decreasing and non-increasing.

It is possible for a function to be neither strictly increasing nor strictly decreasing.

Q. Which of the following graphs shows a function that is non-increasing but is not strictly decreasing?

Q. Which of the following graphs shows an even function?

Q. Which of the following functions is odd?

Q. Which of the following statements is true?

A function must be either even or odd.

A function cannot be both even and odd.

It is possible for a function to be neither even nor odd.

If a function is not even, then that function must be odd.

Q. Which graph shows a function that is strictly decreasing, odd, and bounded both above and below?

A

B

C

D