Translations of Parent Functions
Constant Functions:
f(x) = a+k
Linear Functions:
f(x) = x+k
Absolute Value Functions:
f(x) = |x|+k
Greatest Integer Functions:
f(x) = [x]+k
Quadratic Functions:
f(x) = x²+k
Cubic Functions:
f(x) = x³+k
Square Root Functions:
f(x) = √x+k
Cube Root Functions:
f(x) = ∛x+k
Constant Functions:
f(x) = a+k
- k>0 move up k units
- k<0 move down k units
- Reflect across the x-axis
Linear Functions:
f(x) = x+k
- k>0 move up k units
- k<0 move down k units
- Horizontal shrink/stretch
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the y-axis
- Reflect across the x-axis
Absolute Value Functions:
f(x) = |x|+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
- Reflect across the y-axis
Greatest Integer Functions:
f(x) = [x]+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
- Reflect across the y-axis
Quadratic Functions:
f(x) = x²+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
- Reflect across the y-axis
Cubic Functions:
f(x) = x³+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
Square Root Functions:
f(x) = √x+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
- Reflect across the y-axis
Cube Root Functions:
f(x) = ∛x+k
- k>0 move up k units
- k<0 move down k units
- h>0 move left h units
- h<0 move right h units
- Horizontal stretch/shrink
- a>1 horizontal shrink
- 0<a<1 horizontal stretch
- Vertical shrink/stretch
- a>1 vertical stretch
- 0<a<1 vertical shrink
- Reflect across the x-axis
- Reflect across the y-axis