1. 2.2 Vertical and Horizontal Shifts of Graphs

2. Quiz
Identify the basic function with a graph as below:

3. Vertical Shift of graphsy
Discussion 1
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?

4. Vertical Shift of Graphs
Discussion 2 y
f(x) = x3
↑ 2 unit
f(x) = x3+2
↓ 3 unit
f(x) = x3-3 x

5. 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

6. Horizontal Shift of graphsy
Discussion 1
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?

7. Horizontal Shift of Graphs
Discussion 2 y
f(x) = |x|
← 2 unit
f(x) = |x + 2|
→ 3 unit
f(x) = |x - 3| x

8. 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)

9. Conclusion ↑ f(x) + c → f(x - c) ↓ f(x) - c f(x + c) ← y f(x) + c f(x)

10. 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.)

11. 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

12. Combinations of vertical and horizontal shiftsy
Graph  equation
Write the equation for the graph below. Assume each grid mark is a single unit.
Answer:
f(x) = (x-1)3-2 x

13. Combinations of vertical and horizontal shiftsy
Equation  graph
Sketch the graph of
y = f(x) = √x-2 -1.
How does the transformation affect the domain and range? x
Step 1: f(x) = √x
Step 2: f(x) = √x-2
Step 3: f(x) = √x-2 -1

14. 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

15. 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 )  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 )  Correspondingly, the deadline for full credit for Skills Test #1 is moved to Tuesday, February 15.

16. Homework PG. 99: 3-45(M3), 47-65(odds) KEY: 18, 27, 49, 51
Reading: 2.3 Stretch, Shrink & Reflect