1. Warm-up: Common Errors → no-no’s!
Explain the error in each problem:
1) (–5)2 = –25
2) –52 = 25
3) –2(3)2 = –62

2. HW Key: p. 94: (even), 54, 60, 68, 70
44. a) b) 46. g(–3) = 1; g(0) = 0; g(2) = 5; g(5) = – even 50. odd 52. neither 54. even 60. odd 68. y-axis 70. neither

3. Unit 2: Graphical Analysis of Functions
2.2 Vertical & Horizontal Shifts of Graphs – Part 1

4. Objectives & HW:
Students will be able to shift graphs vertically and horizontally.
HW: p. 100: 17-19, 20, 22, 24, 32, 36, 40, 42
Note: Students need graph paper for #’s 32, 36, 40, and 42.

5. Graph the following on the same set of axes:
Vertical Shifts:
Graph the following on the same set of axes: ● ● ●
Make sure to put the parent function points (ordered pairs) and the transformed points on the board. Let the students come up (discover) the algebraic transformation for both the x- and y-coordinates. For both transformations, x remains as x while y becomes y + 3 for #2 and y – 3 for #3.

6. Graph is shifted upward c units.
Vertical Shift Rules:
Graph is shifted upward c units.
Graph is shifted downward c units.

7. Graph the following on the same set of axes:
Horizontal Shifts:
Graph the following on the same set of axes: ● ● ●

8. Horizontal Shift Rules:
Graph is shifted right c units.
Graph is shifted left c units.

9. Combinations of Vertical & Horizontal Shifts:
1. Graph:
Describe the transformations in words:
Transform the points:
Parent
Transformed x y 1 4 2 9 3

10. Combinations of Vertical & Horizontal Shifts:
2. Graph:
Describe the transformations in words:
Transform the points:
Parent
Transformed x y –2 4 –1 1 2

11. Combinations of Vertical & Horizontal Shifts:
3. Graph:
Describe the transformations in words:
Transform the points:
Parent
Transformed x y –2 2 –1 1

12. How is the graph of each of the following functions obtained from the graph of y = f(x)?
a) g(x) = f(x) + 4
b) h(x) = f(x + 4)