Transformation Connections
For each given function:
 draw the transformed function on the same grid
 write the mapping notation for the transformation (how the points change)


write the equation of the transformed function in function notation, y  af b  x  c    d
describe the transformation (horizontal, vertical, stretch, reflection, translation).
1. Linear function, f  x   x becomes y  2 x
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
2. Sinusoidal function, f  x   sin x becomes y  2sin x
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
3. Quadratic function, f  x   x2 becomes y   x 2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
4. Sinusoidal function, f  x   sin x becomes y   sin x
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
5. Logarithmic function, f  x   log2 x becomes y  log2  2 x 
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
6. Sinusoidal function, f  x   sin x becomes y  sin  2 x 
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
7. Radical function, f  x   x becomes y   x
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
8. Sinusoidal function, f  x   sin x becomes y  sin   x 
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
9. Rational function, f  x  
1
1
becomes y 
x
x2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
10. Sinusoidal function, f  x   sin x becomes y  sin  x  2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
11. Exponential function, f  x   2x becomes y  2 x  2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
12. Sinusoidal function, f  x   sin x becomes y  sin x  2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
13. Absolute value function, f  x   x becomes y  2 x  2
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
14. Sinusoidal function, f  x   sin x becomes y  sin  2 x  2 
mapping notation
 x, y  
equation in y  af b  x  c    d
describe the transformation.
Conclusions:
Mapping
Notation
Original
Function
General Function
 x, y 
y  f  x
x

  c, ay  d 
b

y  af  b  x  c    d
Sinusoidal Function
y  sin x
or
y  cos x
Horizontal
stretch
Vertical
stretch
Horizontal
reflection
Vertical
reflection
Horizontal
translation
Vertical
translation
Generally
y  a sin b  x  c    d
y  a cos  b  x  c    d