Step 4 Using multiple representations, describe the pattern. Cut and sort the following data tables that students collected from difference sequences. Step Amount 1 2 2 6 3 18 4 54 Step Amount 1 4 2 12 3 24 4 40 Step Amount 1 2 2 5 3 8 4 11 Step Amount 1 1 2 8 3 27 4 64 Step Amount 1 3 2 15 3 75 4 375 Step Amount 1 20 2 10 3 5 4 5/2 Step Amount 1 1 2 5 3 9 4 13 Step Amount 1 1 2 4 3 9 4 16 Step Amount 1 3 2 5 3 7 4 9 Tape or paste in your categories here.
Step Amount 1 2 2 4 3 6 4 8 Step Amount 1 4 2 12 3 36 4 108 Step Amount 1 1 2 4 3 7 4 10 Step Amount 1 64 2 16 3 4 4 1 Step Amount 1 3 2 15 3 75 4 375 Step Amount 1 20 2 10 3 5 4 5/2 Step Amount 1 1 2 5 3 9 4 13 Step Amount 1 1 2 6 3 11 4 16 Step Amount 1 3 2 5 3 7 4 9 Practice Set 11 Name _______________________ 1. If a table of values appears to have a common ratio or factor, what type of sequence does the table represent? Explain your response. 2. Is the equation a recursive or explicit definition? Explain your response. Explain the meaning of the equation in terms of a sequence. 3. Use different representations to determine the next term in the sequence. Step 1 Step 2 Step 3 Use function notation to write a recursive definition.
If the sequence continues, will position 3 ever have a different term? Explain. These sequences are examples of functions. Domain: Input: position What are possible positions? Write a sentence beginning with “The domain of the previous function is …” Range: Output: terms For the last sequence, what are the possible terms? Write a sentence beginning with “The range of the previous function is… “ Function As a group, consider the following sets. Determine whether each is a function or not. Explain. 1. A student’s name versus their school ID number. 2. A school ID number versus a student’s last name. 3. The cost of gas versus the amount of gas pumped. 4. 5. The time of day with respect to the temperature. 6.
ACT Warm-Up Given the following quadrilateral and its reflection, discuss methods to find the mirror line. Take notes on the discussion. Make additional comments or corrections during discussion. Discuss methods for finding the midpoint. For each figure, describe where a mirror line would have to be to reflect the image onto itself?
Rotations Write two sentences to describe what rotations do. Write one sentence to say whether or not rotations can be modeled with functions. Make additional comments or corrections during class discussion. Write one sentence to answer the following question: Do you believe that rotations produce congruent figures? Triangle ABC has vertices at (1,3), (4,7), and (5,0). Rotate triangle ABC about the origin. Write a function that describes the rotation. Use the class techniques to determine whether or not the triangles are congruent.
5. 3x – 5 = 7 + 3x 6. x – 2 = 3x – 6 7. 2(x – 4) = 7x – 10 8. 8 – 2x + 3 + 5x = 10(x + 1) – 13x
Practice Set 52 Name_________________________ 6. Just how accurate are the weather forecasts we hear every day. The table below compares the daily forecast with the city’s actual weather for a year. Forecast Actual Weather Rain No Rain Total Rain 27 90 No Rain 268 Total 365 a. On what percent of days did it actually rain? b. On what percent of days was rain predicted? c. What percent of the time was the forecast correct? d. Do you see evidence of an association between the type of weather and the ability of forecasters to make an accurate prediction? Write a brief explanation, including an appropriate graph.
2) Representations of Categorical Data Are you a lefty or a righty? Symbols 2-way Table Key: Male = M Female = F Lefty = L Righty = R Sample size = P(L) = P(M) = P(F) = P(L|F) = P(L|M) = In this sample are there equal proportions of males and females who are left handed? Explain. Is “handedness” independent from gender? How do you know? Venn Diagram Tree Diagram Practice Set 54 Name_________________________ 3) Representations of Categorical Data Do you eat breakfast or not? Symbols 2-way Table Key: Male = M Female = F Eats Breakfast = E Doesn’t Eat Breakfast =