1.2.6What can you do for your country?

Design a Flag

1-92.

DESIGN A FLAG

A tiny country, Minima, is finally about to receive recognition from the United Nations! However, before the ceremony is held to make Minima an official country a special flag needs to be designed.

The new president has bestowed upon you the responsibility of designing the flag. He does not want just a colorful flag—he also wants it to have a unique shape. He also wants a flag that when rotated has a volume of $18π \text{ un}^3$ , as there are $18$ states that make up the nation of Minima.

Design a horizontal flag that when rotated has a volume of $18π \text{ un}^3$ . The more interesting and complicated the design, the more appreciative the president will be!
Write a set of piecewise-defined functions for its shape. These will be the instructions to the flag seamstress.
Explain how you chose your design. What problems did you encounter?

1-93.

Sketch the graph of a function with a domain of $−2 ≤ x < 6$ and a range of $y > 2$ . Then sketch a second possible function. 1-93 HW eTool (Desmos). Homework Help ✎

1-94.

If $f(x) = (x - 3)^2 + 4$ and $g(x) =\frac { 1 } { x - 4 }-2$ , write explicit equations for the following transformations. Homework Help ✎

$h(x) = f(x + 2) - 5$
$k(x) = g(3 - x) + 2$
Use set notation to state the domains and ranges of $h$ and $k$ .

1-95.

Use what you know about transformations of functions to sketch graphs of the following functions. Verify that your graphs are correct on your graphing calculator. Homework Help ✎

$y = (x - 2)^2 + 1$
$y =\frac { 1 } { 2 }(x - 1) - 5$
$y = -| x - 4 |– 6$
$y = 2^{x+1} + 3$
State the domain and range of the function in part (d). Then state the domain and range of its inverse.
Which of the functions above have inverses that are not functions?
Explain how you know.

Calculus Third Edition