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

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 + 1 or f(x) = x – 2

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

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

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

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

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

Can you make any predictions? See any patterns? RECAP f(x) = (x ─ 2)2 Shifts to the right 2 along the x-axis f(x) = (x + 3)2 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

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

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

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