1. Section 5.1 Vertical and Horizontal Shifts

2. In your groups fill in the following table
Plot each of these functions on the same set of axes
Several groups should put their plots up on the board x 1 2 3 4 5 6
f(x) -5 -3 7 12
f(x + 1)
f(x - 1)
f(x) + 1
f(x) - 1

3. Plot f(x) = x2 – 3 and g (x) = x2 – 6x + 1 on the same set of axes
What is the relationship between the two graphs?
If we rewrite g(x) as g(x) = (x – 3)2 – 3 – 5 we can see it as f(x) being shifted. What is the shift?
3 units to the right and 5 units down

4. Consider the following two functions:
What kind of shift is there between the first function and the second?
Graph them together using the window ≤ x ≤ 5, 0 ≤ y ≤ 3
Does it still look like a horizontal shift?

5. In general f(x + a) is a shift a units to the left
f(x – a) is a shift a units to the right
f(x) + a is a shift a units up
f(x) – a is a shift a units down

6. Consider the following two functions:
What kind of shift is there between the first function and the second?
Write f(x) as both a vertical and horizontal shift

7. Work on problem 36 in your books
Be prepared to share your solutions
Try the following problems in your groups: 5, 6, 20, 22