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

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 domain of f is all values of x from -9 to 9.

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

The range of f is the single number 1.

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

f is a function. No single value of x is related to more than one value of y.

4. Is f continuous over its domain? Explain.

Yes, f is continuous over its domain. There are no gaps in its range.

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

Hardly!

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

f is neither increasing nor decreasing. It is a constant function.

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

f is neither increasing nor decreasing. It is a constant function.