$\DeclareMathOperator{\asin}{asin}$ $\DeclareMathOperator{\acos}{acos}$ $\DeclareMathOperator{\atan}{atan}$

The animation below shows values of x being related to values of y by a relationship named f. Play the video, then answer the questions following the video using meanings for terms in the question. You can replay the video and pause it, or scroll the play bar to examine parts of the video. (Move your pointer away from the video to remove the scroll bar.)

1. What, approximately, is the domain of f?

The value of x appears to vary through all values from -6 to 6. Each of these values is related to a value of y. The domain of f is therefore all values of x such that $-6\le x \le 6$. It does not matter that x takes on values more than once. A value is in the domain of f no matter how many times x has this value.

2. What, approximately, is the range of f?

The value of y appears to range from -8 to 8 as x takes on values from -6 to 6. It does not matter that y takes on the same value for different values of x.

3. Is the relationship named f a function from x to y? Explain.

No, f is not a function from x to y. $f(0)=-8$ and $f(0)=8$. Therefore, it is not the case that every value in the domain of f is related to exactly one value in the range of f.

4. Is f continuous over its domain? Explain.

This question is irrelevant because f is not a function. Continuity is an issue only when a relationship is a function. There is no way to capture all values of $f(x)$ within a tolerance of $\epsilon =0.5$ over any interval containing $x=0$.

5. Is f one-to-one over its domain? Explain.

This question is irrelevant because every value of x in the domain of f except -8 and 8 has two values of y associated with each value of x.

6. Over what interval(s) in its domain, if any, is f increasing? Explain.

This question is irrelvant because each value of x in the domain of f except -8 and 8 has two values of y associated with it. In a sense, values of $f(x)$ increase and decrease simulaneously.

7. Over what interval(s) in its domain, if any, is f decreasing? Explain.

This question is irrelvant because each value of x in the domain of f except -8 and 8 has two values of y associated with it. In a sense, values of $f(x)$ increase and decrease simulaneously.