Unit 6 Note Packet List of topics for this unit/assignment tracker Date Topic Assignment & Due Date Absolute Value Transformations Day 1

Transcription

1 Name: Period: Unit 6 Note Packet List of topics for this unit/assignment tracker Date Topic Assignment & Due Date Absolute Value Transformations Day 1 Absolute Value Transformations Day 2 Graphing Equations Activity Solving Absolute Value Equations Solving Absolute Value Equations by Graphing Practice Test/Review Test 1

2 Absolute Value Transformations- Day 1 The Absolute Value Function (called the absolute value parent function) Date: x y Table: Graph: Translations: Absolute Value Equation Prediction of transformation (how will the graph of the parent function change?) Graph (both parent and transformation) If you were correct-name one hint for a classmate. If you were wrong where did you make your mistake. 1. yy = xx 4 2. ff(xx) = xx + 1 2

3 3. yy = xx yy = xx 4 5. ff(xx) = xx gg(xx) = xx

4 Summary Horizontal shift (x-shift): Vertical shift (y-shift): ff(xx) = aa xx h + kk Describe how the graph of the parent function will change, then graph (without technology). 1. yy = xx ff(xx) = xx gg(xx) = xx Description: Description: Description: 4

5 Absolute Value Transformations Day 2 Date: Warm-up: 1. Write an equation of the absolute 2. Write an equation of the absolute 3. If you translate the function value graph shown: value graph shown: ff(xx) = xx to the right six units and down 8 units, what would the new equation be? Translations: Absolute Value Equation Prediction of transformation (how will the graph of the parent function change?) Graph (both parent and transformation) If you were correct-name one hint for a classmate. If you were wrong where did you make your mistake. 1. yy = xx 2. ff(xx) = 1 2 xx 5

6 3. yy = 3 xx 4. yy = xx ff(xx) = 2 xx gg(xx) = 3 2 xx 1 2 6

7 Summary Vertical reflection: a > 0 : a< 0 : ff(xx) = aa xx h + kk Vertical stretch/compress: a > 1 : a} < 1 : 1.Graph: yy = xx ff(xx) = 3 xx Write the 4 equation of the graph Description: Description: 7

8 Absolute Equations Graphing Activity Date: Part 1: Graphing absolute value functions My group s absolute value equation is: The graph looks like: (neatly and accurately create a copy of your graph on the graph paper provided, including the number and post on a wall in the room) Part 2: Writing equations of absolute values functions Find 8 absolute value graphs posted around the room and write the equation for the graph shown. Be sure to include the number of the graph your group chose. Part 3: Reflection 1. The easiest part of graphing absolute value functions is: Because: 2. The hardest part of graphing absolute value functions is: Because: 3. The most important thing to remember about graphing absolute value functions is: 8

9 6.5 Solve Absolute Value Equations Date: Vocabulary Absolute Value Equation Guided Practice 1. Solve xx = 7 Your Turn Solve 2. xx = 3 3. xx = 15 Solving an Absolute Value Equation Guided Practice 4. xx 3 = xx 5 = 18 Your Turn 6. rr 7 = xx + 7 = 11 9

10 Guided Practice xx 7 5 = 4 Your Turn 9. 2 ss = tt = 19 Guided Practice 11. Solve 3xx = 2, if possible. Your Turn Solve the equation, if possible mm = nn = 10 10

11 Solving Absolute Value Equations by Graphing Date: 1 EXAMPLE Solving an Absolute Value Equation by Graphing Solve the equation 2 x = 5 by graphing. A Treat the left side of the equation as the absolute value function f(x) = 2 x Graph the function by following these steps. Identify and plot the vertex: If you move 1 unit to the left or right of the vertex, describe how must you move vertically to get to a point on the graph. Give the coordinates of these points and then plot them. Use the three plotted points to draw the complete graph. B Treat the right side of the equation as the constant function g(x) = 5. Draw the graph of g(x) on the same coordinate plane as the graph of f(x). C Identify the x-coordinate of each point where the graphs of f(x) and g(x) intersect. Show that each x- coordinate is a solution of 2 x = 5. B Interpret the equation x 3 = 2: What numbers have an absolute value equal to 2? 11