1. Predicting Changes in Graphs
f(x) = x2
f(x) = |x|
f(x) = x
Along the x-axis!
Cain 10’08

2. Transformations along the X-axis
Occur when constant terms are added within the main function
For f(x) = x2, it would be within the square (2)
For f(x) = |x|, it would be within the absolute value signs
For f(x) = x, it would be within the root sign
Ex: f(x) = (x + 1)2 or f(x) = (x – 2)2
Ex: f(x) = |x + 3| or f(x) = |x – 1|
Ex: f(x) = x or f(x) = x – 2

3. Tables of input and output
Let's graph it!
input
(x - 2)2
output f(x) 4 1 x 3
(3 - 2)2
(0- 2)2 1
(1 - 2)2 2
(2 - 2)2

4. Here’s a graph of the original function
f(x) = x2
Here’s a graph of the original function

5. The graph shifted right 2 units along the x-axis
f(x) = x2
(0,4)
f(x) = (x ─ 2) 2
(1,1)
(3,1)
(2,0)
The graph shifted right 2 units along the x-axis

6. Let’s do another one! x -3 -2 -1 -4 (x + 3)2 1 4 (-3 + 3)2 (-2 +3)2
Let's graph it!
input
output f(x) x -3 -2 -1 -4
(x + 3)2 1 4
(-3 + 3)2
(-2 +3)2
(-1 +3)2
(-4 +3)2

7. The graph shifted left 3 units along the x-axis
f(x) = (x +3)2
(-1,4)
(-4,1)
(-2,1)
(-3,0)
The graph shifted left 3 units along the x-axis

8. Can you make any predictions? See any patterns?
RECAP
f(x) = (x ─ 2) Shifts to the right 2 along the x-axis
f(x) = (x + 3) Shifts to the left 3 along the x-axis
Can you make any predictions? See any patterns?
Changes in the main function shift the opposite direction of their sign along the x-axis

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

10. 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 left 2 along the x-axis
Shifts right 1 along the x-axis

11. 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 right 1 along the x-axis
f(x)= x
Shift left 2 along the x-axis