1) f(x) = (x-1)³ + 2
Base function: x³
Transformations: Shift right 1, up 2
New origin: (1, 2)
T-chart:
x | x³
-2 | -8
-1 | -1
0 | 0
1 | 1
2 | 8
2) f(x) = -3√(x+4)
Base function: √x
Transformations: Stretch vertically by 3, flip down, shift left 4
New origin: (-4, 0)
T-chart:
x | √x
0 | 0
1 | 1
4 | 2
3) p(x) = (2x)²
Base function: x²
Transformations: Shrink horizontally by 1/2
New origin: (0, 0)
T-chart:
x | x²
-1 | 1
-1/2| 1/4
0 | 0
1/2| 1/4
1 | 1
4) k(x) = (2-x)³ - 3
Base function: x³
Transformations: Flip across y-axis, shift right 2, down 3
New origin: (2, -3)
T-chart:
x | x³
-2 | -8
-1 | -1
0 | 0
1 | 1
2 | 8
5) r(x) = 2|x+3| - 5
Base function: |x|
Transformations: Stretch vertically by 2, shift left 3, down 5
New origin: (-3, -5)
T-chart:
x | |x|
-2 | 2
-1 | 1
0 | 0
1 | 1
2 | 2
6) w(x) = √(1/2 x) - 3
Base function: √x
Transformations: Stretch horizontally by 2, shift down 3
New origin: (0, -3)
T-chart:
x | √x
0 | 0
2 | √2
4 | 2
8 | 2√2
7) math(x) = -1/(x+4) - 3
Base function: 1/x
Transformations: Flip across x-axis, shift left 4, down 3
New origin: (-4, -3)
T-chart:
x | 1/x
-2 | -1/2
-1 | -1
0 | undefined
1 | 1
2 | 1/2
Parent Tip: Review the logic above to help your child master the concept of advanced algebra graph transformations worksheet.
