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2.2 Vertical and Horizontal Shifts of Graphs 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 f(x) = x2-5 ↓ 5 unit What about shift f(x) up by 10 unit? shift f(x) down by 10 unit? x Vertical Shift of Graphs Discussion 2 y f(x) = x3 ↑ 2 unit f(x) = x3+2 ↓ 3 unit f(x) = x3-3 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 f(x) = (x-5)2 → 5 unit What about shift f(x) left by 10 unit? shift f(x) right by 10 unit? x Horizontal Shift of Graphs Discussion 2 y f(x) = |x| ← 2 unit f(x) = |x + 2| → 3 unit f(x) = |x - 3| 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) ← f(x) ↓ f(x) + c → f(x - c) x 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 y Write the equation for the graph below. Assume each grid mark is a single unit. Answer: f(x) = (x-1)3-2 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 inclass 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