Horizontal Shift
The function below shifts in this direction
1/(x-3)
What is Right
The function below vertically transforms in this direction
1/x + 4
What is Up
Stretch or Compress?
3/x
Stretch
Horizontal Shift of
2/(x + 16) - 3
16 Left
When graphing, the two dotted lines that the hyperbola approach are called this
What are asymptotes
1/(x+5)
What is 5 Left
Vertical Shift
1/x -15
Down 15
Stretch or Compress
1/(2x)
Compress
Horizontal and Vertical Shift
1/(x - 6) + 13
Right 6
Up 13
When making a table to graph, the first two columns are this
Horizontal Shift of:
1/(x +16) - 3
What is Left 16
Vertical Shift
1/(x - 9) - 14
Down 14
y = ? when x = 2
y = 2/x
y = 1
All Transforms
10/(x-4) + 13
Horizontal: 4 Right
Stretch: 10
Vertical: 13 Up
What happens to this graph?
-1/x
The hyperbola flips to the other sides of the asymptotes
Horizontal Shift of
1/(x - 1) + 12
What is 1 Right
Verical Shift
1/(x + 2) + 3
Up 3
y = ? when x = -2
4/x
y = 1/2
All Transforms
8/(x+3) + 12
Horizontal: Left 3
Stretch: 8
Vertical: Up 12
What are the horizontal and vertical asymptotes?
4/(x+3) - 10
HA: y = -10
VA: x = - 3
Horizontal Shift
5/(9 + x)
What is Left 9
Vertical Shift
20 + 1/(x - 1)
Up 4
Stretch of:
3/(x - 5) + 12
3 Stretch
All Transforms
1/(4(x+1)) - 12
Horizontal: 1 Left
Stretch: 1/4
Vertical: 12 Down
What order are transformations applied?
1. Horizontal Shift
2. Stretch/Compress
3. Flip
4. Vertical Shift