Tissue Box Assignment
1st Nine Weeks Math Challenge

The assignment is worthup to2% added to your final nine weeks grade if each part is completed correctly and accurately. Please avoid completing this the night before the assignment is due. Only thoughtful and neat assignments will be graded.
Due: Thursday, Oct. 5th - No Exceptions! In fact, you are welcome and encouraged to turn it in early!

1.)On a new box of tissue, cover each of the four sides excluding the top and bottom, with paper. Write your name on the bottom of the box.

2.)Choose a topic and write it on one of the four sides. AP Calculus – You may choose any topic from Chapter 2. Honors Precalculus – You may choose any topic from Chapters 2 or 3. On the remaining three sides, represent your topic graphically, numerically, and algebraically. An example is given below.

Topic:
The Reciprocal Function / Graphically:
/ Numerically:
x / f(x)
-2 / -½
-1 / -1
-½ / -2
0 / Und
½ / 2
1 / 1
2 / ½
/ Algebraically:

3.)Using the MPACs (Mathematical Practices for AP Calculus), write threerich problems about your chosen topic and include their solutions. Your problems may need to have multiple parts and steps in order to fulfill the objective. Cite which MPAC and objective you are applying. You must use objectives from three different MPACs. (For example, MPAC #1b, #3c, and #6d.) The MPACs are posted on my website and in the classroom. An example problem is given below:

MPAC 1 – e: develop conjectures based on exploration with technology

Problem #1:
Use your graphing calculator to answer these questions.

a.) In the same viewing window, graph and . Describe any changes to the graph making note of characteristics such as asymptotes, domain, and range.

b.) In the same viewing window, graph and . Describe any changes to the graph making note of characteristics such as asymptotes, domain, and range.

c.) Based on the results from (a) and (b), what can you conclude about the asymptotes, domain, and range of ?
Solution to problem #1:
Use your graphing calculator to answer these questions.

a.) In the same viewing window, graph and . Describe any changes to the graph making note of characteristics such as asymptotes, domain, and range.
The graph of has been shifted up 2 units. The V.A. is still at x = 0 and the domain remains as . The H.A. is now at y = 2 and the range has changed to .

b.) In the same viewing window, graph and . Describe any changes to the graph making note of characteristics such as asymptotes, domain, and range.
The graph of has been shifted to the left 2 units. The H.A. and range remain unchanged. The H.A. is y = 0 and the range is . The V.A. is now at x = -2 and the domain is .

c.) Based on the results from (a) and (b), what can you conclude about the asymptotes, domain, and range of ? Explain your reasoning.
The V.A. will be x = h and the H.A. will be y = k. The domain will be and the range will be . The h-value provides a horizontal shift (If h < 0, the shift is h units to the left. If h > 0, the shift is h units to the right), causing a change in the domain. The k-value provides a vertical shift (If k > 0, the shift is k units up. If k < 0, the shift is h units down.), causing a change in the range.