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

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

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

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

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

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

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

Predicting Changes in Graphs f(x) = x Linear f(x) = x2 Nonlinear f(x) = |x| Nonlinear f(x) = x Nonlinear

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

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

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

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

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

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 up 2 along the y-axis Shifts down 1 along the y-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 down 1 along the y-axis f(x)= x Shift up 2 along the y-axis