1. Predicting Changes in Graphs
Called transformations
Concentrate on 4 graphs, called Parent Graphs
1st Parent Graph:
f(x) = x
Cain 10’08
Along the y-axis

2. Tables of input and output
output = f(x) x
f(x)=x -2 1 2
Let's graph it!

3. f(x) = x
(2,2)
(1,1)
(0,0)
(-2,-2)

4. Tables of input and output
output f(x)
x ─ 1
output f(x) -1 -3 1 x
f(x)=x -2 1 2

5. The graph shifted down 1 unit along the y-axis
f(x) = x
f(x) = x ─ 1
The graph shifted down 1 unit along the y-axis

6. Tables of input and output
x ─ 1
output -1 -3 1
x + 1
output 1 -1 2 3 x
f(x) -2 1 2

7. The graph shifted up 1 unit along the y-axis
f(x) = x
f(x) = x + 1
The graph shifted up unit along the y-axis

8. Predicting Changes in Graphs
f(x) = x Linear
f(x) = x Nonlinear
f(x) = |x| Nonlinear
f(x) = x Nonlinear

9. Tables of input and output
output f(x) x
f(x)=x2 -2 4 1 2
Let's graph it!

10. f(x) = x2
(-2,4)
(2,4)
(1,1)
parabola
(0,0)

11. Tables of input and output
output f(x)
x2 ─ 2
output f(x) -2 2 -1 x
f(x)2 -2 4 1 2

12. The graph shifted down 2 units at the y-axis
f(x) = x2
f(x) = x2 ─ 2
(2,2)
(-2,2)
(1,-1)
(0,-2)
The graph shifted down 2 units at the y-axis

13. What transformation will happen if we add 3 to this parent graph?
Parent Graph f(x) = x2
What transformation will happen if we add 3 to this parent graph?
f(x) = x2 + 3
The graph will shift up 3 units along the y-axis

14. Other 2 parent graphs are:
f(x) = |x| Nonlinear
f(x) = x Nonlinear
f(x)=|x|
f(x)= x

15. f(x) = |x| f(x) = |x| + 2 f(x) = |x| - 1 f(x)=|x|
What would happen to the graph if it was:
f(x) = |x| + 2
What would happen to the graph if it was:
f(x) = |x| - 1
f(x)=|x|
Shift up 2 along the y-axis
Shifts down 1 along the y-axis

16. f(x) = x f(x) = x + 2 f(x) = x - 1 f(x)= x
What would happen to the graph if it was:
f(x) = x + 2
What would happen to the graph if it was:
f(x) = x - 1
Shifts down 1 along the y-axis
f(x)= x
Shift up 2 along the y-axis