MRS. PROFIO-MILLER'S MATH WEBSITE - Home



Common Core IMrs. Profio-MillerName: _______________________Unit 3: FunctionsDayDateTopicGrade (Teacher fills in – 1 stamp is 1 point for ? work, 2 stamps = 2 points for all work)AB1Wed.,October 9th Thursday,October 10th Unit 3 Pre-AssessmentRecursive Patterns (NOW NEXT)HW: pg. 22Friday, October 11thMonday, October 14th Explicit Patterns (INPUT OUTPUT) HW: pg. 3-43Tuesday, October 15th Wed., October 16th Define function/function notation Evaluating FunctionsHW: pg 5-64Thursday, October 17th Friday, October 18th Early ReleaseQUIZ on Day 1 -3 MaterialDomain and Range of FunctionsHW: pg 75Monday, October 21st Tuesday, October 22ndInterpreting Graphs Rate of ChangeHW: pg. 86Wednesday, October 23rd Thursday, October 24th Extension: TranslationsReviewHW: pg 9 – 11Go over review sheet – Study for test!584207289807Friday, October 25th Tuesday, October 29th TEST TODAY(This packet will be collected today!) REMINDER….check class website for helpful links and copies of notes! profiomillermath.(Click on Common Core Math 1 Unit 3)Come to see Mrs. P.M. for tutoring on Tuesdays and Wednesdays 2:30 – 3:30 pmGo to SAS Curriculum Pathways (login: BroughtonStudent) Use the Quick Launch numbers 5031, 5032, and 5033 (to access these, type in the top right of the homepage where it says QL # )Unit 3 Day 1 Homework: Recursive PatternsName: __________________Consider the sequence of figures below made from plete the table below for the first five figures.FigureNumberPerimeter1325345Write a NOW-NEXT equation to find the perimeter of each figure. ___________________Find the perimeter of the 10th figure. _________________________Which number figure has a perimeter of 51? _____________________Look at the student’s calculator screen below. Try to figure out the first six values generated by the recursive routine of the student pressing ENTER. Then write the routine as a NOW-NEXT equation.Write a NOW-NEXT equation for each sequence. Then use your equation to find the 8th term of each sequence.7.8, 3.6, -0.6, -4.8, . . . b.) 1, 3, 9, 27, . . .c.) -9.2, -6.5, -3.8, -1.1, . . . d.) 36, 12, 4, 43 , . . .Unit 3 Day 2 Homework: Explicit PatternsName: __________________Part I: For each section below, fill in the table of values or graph the points given. Then write the NOW-NEXT equation for each relationship AND the INPUT-OUTPUT equation.xy00.511.522.533.544.54019550730252914650187325476250158750 b.) NOW – NEXT equation: NEXT = ____________NOW – NEXT equation: NEXT = ___________INPUT-OUTPUT equation: OUTPUT = ___________INPUT-OUTPUT equation: OUTPUT = ________41243251282702095501320806191250132080xy0113253749c.) d.) NOW – NEXT equation: NEXT = ___________ NOW – NEXT equation: NEXT = ____________INPUT-OUTPUT equation: OUTPUT = ___________INPUT-OUTPUT equation: OUTPUT = ________Part II Find the first five terms for each NOW NEXT sequence.START = -22.) START = 13.) START = 6NEXT = NOW +7 NEXT = NOW*3 NEXT = NOW*2 + 4Fill in the tables below for each INPUT-OUTPUT rule. Then write the rule using x and y.4.) OUTPUT = INPUT*7 + -25.) OUTPUT = 3INPUT6.) OUTPUT = INPUT*2 + 4INPUTOUTPUT01234INPUTOUTPUT01234INPUTOUTPUT01234Rule: _____________Rule: ______________Rule: _______________Compare the NOW-NEXT and INPUT-OUTPUT rules from Part II #1-7. What do you notice?Which above patterns are in explicit form? _________________________Which above patterns are in recursive form? ______________________Unit 3 Day 3 Homework: Functions/Mid-Unit ReviewName: __________________Use the described pattern to find the first 5 terms of the number sequence. Then write a NOW-NEXT or INPUT-OUTPUT equation for each.Each term of the sequence is found by adding 5 to the preceding term. The starting number is 3.Term12345Number Write a recursive equation: _______________________Each term of the sequence is found by multiplying the term number by 7 and adding 3 to the result. The starting number is 6.Term12345NumberWrite an explicit equation: _______________________Each term of the sequence is found by multiplying the preceding term by 12. The starting number is 80.Term12345NumberWrite a recursive equation: _______________________Each term of the sequence is found by multiplying the term number by -2 and subtracting 4 from the result. The starting number is 1. Term12345NumberWrite an explicit equation: _______________________Evaluate the following functions:5.) f(x) = x – 5 for f(3) and f(-4)6.) f(x) = 2x2 – x + 10 for f(3) and f(-4)9525004318004319270Unit 3 Day 4 Homework: Domain and RangeName: __________________47123352514603143253086101. With the given values, find the missing input (domain) or output (range).244792562230a.)b.)c.) 229552521145550878371543052. Are the following functions? If yes, state the domain and range.xy1305-13-21a.) b.) c.) y=f(x)3. Use the graph of y=f(x) at the right to answer each question.What is the value of f4?What is the value of f(6)?For what value(s) does fx=2?For what value(s) does fx=0?For what x-values is f(x) greater than 2?What are the domain and range shown on the graph?Unit 3 Day 5 Homework: Average Rate of ChangeName: __________________2095500308610The graph below represents the distance of the ball in an American football game. Fill in the table and answer the questions using the graph.td(t)0123456 What is the independent variable and the dependent variable?How far did the ball travel from 0 to 2 seconds? What is the average rate of change (distance traveled per minute) for the first two seconds? How far did the ball travel from 2 to 4 seconds? What is the average rate of change (distance traveled per minute) for these two seconds? Is the ball travelling faster during the first 2 seconds or the next 2 seconds? How can you tell? How is this revealed in the graph?When is the ball not moving forward down the field? Where is the graph decreasing? Do you know what happens in football when the ball loses distance?Unit 3 Day 6 Homework: ReviewName: _______________1. Look at the patterns below and fill in the next three terms. Then write a NOW NEXT equation for each patterna. 21, 16, 11, 6, ____, ____, ____b. 2, 8, 32, 128 , ____, ____, ____c. 1.3, 2, 2.7, 3.4, 4.1, ____, ____, ____NEXT =NEXT=NEXT =2. For the INPUT OUTPUT equations given below, fill in the missing values in the tables.Input xOutput y– 1– 5037Input xOutput y– 1005 OUTPUT = 2*INPUT – 3 b. 2x + 4y = 6 40957501498603. Write the following table of values as an INPUT OUPUT equation and then graph the points on the given graph.Input xOutput y-5-2-123658OUTPUT = ___________________5410862186912338328025847218120691630574. Which of the following are functions? Circle (parts a, b, c, d) if it is a function – there’s more than one!XY-24-11001124a.b.c.d5. Given the function f(x) = 3x2 – 1, find f(–5). _______________________________________6. a. Sketch a graph of this situation: The temperature of an ice-cold drink left in a warm room for a period of time. What are the independent and dependent variables?4476750-2857507. Given the graph of f(x), find the following:a.) f(3) = __________b.) What x values make f(x) = 0 ?c.) Where are the output values negative? d.) On the graph, draw the function f(x) translated 2 units up vertically.447675990608. What is the domain and range of the given on the left? 43294301631959. The following graph represents Celia’s marathon race. FWhat is the domain and range of the function? EFind the rate of change in miles per hour for INTERVAL A.DABC During which interval(s) was Celia running the fastest? How do you know?During which interval(s) was Celia resting? How do you know?If Celia maintained the same rate of change as interval A for the entire marathon, how long would it have taken her to finish the race? (A marathon is 26 miles long.)10. Lucille bought a house in 1998 for $144,000. In 2012, the house is worth $245,000. Find the average rate of change in dollars per year of the value of the house. Round your answer to the nearest dollar. 11. If the parent function is y = x2, how is the graph translated if the new equation is y = x2 – 4?12. What is the Fibonacci Sequence? Answers to Review Sheet:1. a) 1, -4, -9 NEXT = NOW – 5 b. ) 512, 2048, 8192 NEXT = NOW*4 c.) 4.8, 5.5, 6.2 NEXT = NOW + 0.7Input xOutput y– 1– 50-333711Input xOutput y– 1201.530-752. a.) b. )23431501758953. OUTPUT = INPUT + 3 or y = x + 3 4. a., d.5. f(-5) = 3(-5)2 – 1 = 746. Independent: time; dependent: temperature7. a.) f(3) = -2b.) f(x) = 0 when x = -2, 1.5, 5419100240665c.) when x < -2 and when x is between 1.5 and 5 d.) 8. domain: -5, -1, 1, 6; range: -5, 0, 3, 59. a.) domain: 0 ≤ x ≤ 6; range: 0 ≤ y ≤ 26b.) 6 miles per hourc.) D – it is the steepest d.) C and E, she was not gaining distancee.) About 4.5 hours10. $245,00-$144,000 = $101000 change over 14 years = 10100/14 = $7214 per year11. Down 4 units 12. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … NEXT = Current term + Previous term ................
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