Algebra 2 Chapter 4 4 1 Warm UP

Algebra 2 Chapter 4

4. 1 • Warm UP: (Vending Machines) •

4. 1 • Investigation: Graph a Story (pg. 186) • If time allows: (pg. 182, 183)

4. 2 Day 1 • Notes: Input, Output, Independent, Depedent • Notes: Function Notation

4. 2 Day 2 • Review Function Notation with BIG warm up: pg. 194 #4

4. 2 Day 2 • • Notes Function : every input has exactly one output Independent Variable : x Dependent Variable : y Domain : the input values (x values) Range : the output values (y values) Vertical Line Test :

4. 2 Day 3 • Warm up: pg. 192

4. 2 Day 3 • Review Vocab • Pre-assessment for rest of chapter (30 minutes, what do you know? )

4. 4 day 1: Parabolas and Translations • Warm up: – If f(x)= 3 x+45, find f(100) • • Alg 1: graph y = x 2 1. y = x 2 +3 2. y = (x-3) 2 Investigation pg. 207: Make my graph Step 2: Step 3: Now go back to the pre-assessment, do #1

4. 4 Investigation

4. 4 Day 2: More translations • Warm UP – Write an equation for each graph • (#6 pg. 210) • Recap of Notes 4. 4 – Inside: input, affects the x values – Outside: output, affects the y values • In class work pg. 210 – #5, 8, 10 • Review each lesson for quiz 4. 1 4. 2, 4. 4

Quiz 4. 1 to 4. 4 Recap Period 1 • 4. 1 – – • 4. 2 – – • 4. 4 – – Absolute Values Input and Output with Function Notation Increase or Decrease Graph Rapid/Slowly Labeling x and y axis Domain and Range with proper notation Independent vs Dependent Variables Vertical Line Test for Functions Definition of Function Identify translations of the vertex Parabola graph Solve equations with Parabolas Translate ANY graph

Quiz 4. 1 to 4. 4 Recap Period 2 • 4. 1 – Tell if a graph is a function – Draw a Graph from description or vice versa – LABEL!! Units, etc. • 4. 2 – Function notation for input and output – Function notation on graphs – DOMAIN and RANGE • 4. 4 – Inside changes x for translations (and outside changes y’s) – Solving parabolic with algebra

Quiz 4. 1 to 4. 4 Recap Period 4 • 4. 1 – Writing stories about graphs – Writing a graph description: increasing, increasing at an increasing rate, increasing at a decrease rate, decreasing at a decreasing rate, etc. – Include arrows, labels on both axes • 4. 2 – Input and Output – Determining if a graph is a function, use the vertical line test – Domain and Range • 4. 4 – – Parabola Translation of Parabolas Arrows on Parabolas Solving with Squares

4. 5 Day 1: Reflections and Square Root Functions • Notes: Graphing the PARENT square root function • Exercise on translations with square roots and parabola’s (Next slide) • Investigation: Take a Moment to Reflect (pg. 213/214) • Step 3 only • Parent is the square root function (f 1(x)) – a) predict y= -f(x) and y = f(-x) – b)predict y = -f(-x)

4. 5 Exercise: translations with square roots and parabola’s

4. 5: Day 2, More reflections • Warm UP: what do you know so far? • What parent functions should we know? • What types of transformations should we know? And how does each look in a parent function? • Practice WS Assignment. Due by end of period. Check answer key when done • Homework: Pg. 216 #4, 5, 6, 8, 11 -13, 16

4. 5: Piecewise Functions • Warm up: Transformation Practice • Notes: Piecewise Functions • Practice (pg. 218, #12) • Example (pg. 215)

4. 5 practice

4. 7: Circles and Ellipses Circle Notes • Define a unit circle • Solve for y and graph • How would we dilate a circle? • How would we horizontally translate a circle? vertically? both? • Example A pg. 229 • Define an ellipse • Example B pg. 230

4. 7 Examples Problems • Example A pg. 229 • Example B pg. 230

4. 8 Day 1: Composition Functions Warm up: • a. Find f(g(1)) • b. Find f(g(-4)) • c. Find f(g(x)) Practice #1 • d. g(f(-1))

4. 7, 4. 8: Recap for Quiz • 4. 7 – Unit Circle – Parent function y= sqrt(1 -x^2) – Ellipses Equation – Translations and Dilations of the y= parent function • 4. 8 – Composition of functions (f(g(#)) or f(g(x)) equation) – Product of functions

4. 7, 4. 8 Recap • 4. 7 – Ellipses – Circles – Dilations = radius – Translations = center – Unit circle x 2+y 2 =1 • 4. 8 – Compositions of functions f(g(x)) equation or for a number as x.

4. 7, 4. 8 Recap • 4. 7 – Unit circle x 2 +y 2 = 1 or y= sqrt(1 -x 2) – General Equation / Ellipse • 4. 8 – Compositions