Create Presentation
Download Presentation

Download Presentation
## 2.2 Vertical and Horizontal Shifts of Graphs

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Quiz**• Identify the basic function with a graph as below:**Vertical Shift of graphs**• Discussion 1 y f(x) = x2 f(x) = x2+1 ↑ 1 unit f(x) = x2-2 ↓ 2 unit x f(x) = x2-5 ↓ 5 unit What about shift f(x) up by 10 unit? shift f(x) down by 10 unit?**Vertical Shift of Graphs**• Discussion 2 y f(x) = x3 f(x) = x3+2 ↑ 2 unit f(x) = x3-3 ↓ 3 unit x**Vertical Shift of Graphs**• If c>0, then the graph of y = f(x) + c is obtained by shifting the graph of y = f(x) upward a distance of c units. The graph of y = f(x) – c is obtained by shifting the graph of y = f(x) downward a distance of c units. ↑f(x) + c ↓f(x) - c**Horizontal Shift of graphs**• Discussion 1 y f(x) = x2 f(x) = (x+1)2 ← 1 unit f(x) = (x-2)2 → 2 unit x f(x) = (x-5)2 → 5 unit What about shift f(x) left by 10 unit? shift f(x) right by 10 unit?**Horizontal Shift of Graphs**• Discussion 2 y f(x) = |x| f(x) = |x + 2| ← 2 unit f(x) = |x - 3| → 3 unit x**Horizontal Shift of Graphs**• If c > 0, the graph of y = f(x + c) is obtained by shifting the graph of y = f(x) to the left a distance of c units. The graph of y = f(x - c) is obtained by shifting the graph of y = f(x) to the right a distance of c units. f(x + c) ← →f(x - c)**Conclusion**y f(x) + c ↑f(x) + c x f(x) f(x + c) ← →f(x - c) f(x + c) f(x - c) ↓f(x) - c f(x) - c**Combinations of vertical and horizontal shifts**• Equation write a description y1 = |x - 4|+ 3. Describe the transformation of f(x) = |x|. Identify the domain / range for both. answer: shifting f(x) up by 3 units, then shift f(x) right by 4 units. ( or shift f(x) right by 4 units, then shift f(x) up by 3 units.)**Combinations of vertical and horizontal shifts**• Description equation Write the function that shifts y = x2 two units left and one unit up. answer: y1 = (x+2)2+1**Combinations of vertical and horizontal shifts**• Graph equation Write the equation for the graph below. Assume each grid mark is a single unit. Answer: f(x) = (x-1)3-2 y x**Combinations of vertical and horizontal shifts**• Equation graph Sketch the graph of y = f(x) = √x-2 -1. How does the transformation affect the domain and range? y x Step 1: f(x) = √x Step 2: f(x) = √x-2 Step 3: f(x) = √x-2 -1**Combinations of vertical and horizontal shifts**• Graph & symbolic transformation new graph Using the given graph of f(x), sketch the graph of f(x) +2 f(x+2) f(x-1) - 3 y x**Math 101 schedule changes**• 1) Project 1 will be a take-home project instead of an in-class group project. The project will be posted by Wednesday, February 9, through the MyKAPInfo link. It is due in class on Monday, February 14.2) Exam 1 for Math 101 will be moved from Feb 15/16 to Feb 16/17. Group A is scheduled for Wednesday, February 16 and Group B on Thursday, February 17. The hours for testing for both days are 7:30 am - 9:00 pm. All exams are in ST 324.3) Correspondingly, the deadline for full credit for Skills Test #1 is moved to Tuesday, February 15.**Homework**• PG. 99: 3-45(M3), 47-65(odds) • KEY: 18, 27, 49, 51 • Reading: 2.3 Stretch, Shrink & Reflect