1. Transformations of exponential functions
LO: Sketch translations, reflections and stretches of exponential function

2. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
g(x) = f(x + 2)
g(x) = 2x + 2
f(x + 2)
f(x)
Move f(x) two units to the left hand side
The y-intersection is translated to (-2, 1)
(-2, 1)
(0, 1)

3. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
h(x) = f(x – 3)
h(x) = 2x - 3
f(x + 2)
f(x)
f(x - 3)
Move f(x) three units to the right hand side
The y-intersection is translated to (3, 1)
(0, 1)
(3, 1)

4. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
In general
f(x + 2)
f(x)
f(x - 3)
f(x + k)
f(x) is translated k units to the left hand side
f(x - k)
f(x) is translated k units to the right hand side

5. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
g(x) = f(x) + 2
g(x) = 2x + 2
f(x)
Move f(x) two units upward
The y-intersection is translated to (0, 3)
f(x) + 2
(0, 3)
(0, 1)

6. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
h(x) = f(x) – 1
h(x) = 2x - 1
Move f(x) one unit downward
The y-intersection is translated to (0, 0)
f(x) + 2
f(x) - 1
f(x)
(0, 1)
(0, 0)

7. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
In general
f(x) + k
f(x) is translated k units upward
f(x) - k
f(x) is translated k units downward
f(x) + 2
f(x) - 1
f(x)

8. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
g(x) = -f(x)
g(x) = -(2x)
f(x)
Reflect f(x) over the x-axis
-f(x)

9. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
h(x) = f(-x)
h(x) = 2-x
f(x)
Reflect f(x) over the y-axis
f(-x)
-f(x)

10. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
In general
f(x)
-f(x)
f(x) is reflected over the x-axis
f(-x)
f(-x)
f(x) is reflected over the y-axis
-f(x)

11. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
g(x) = 2f(x)
f(x) = 2(2x)
2f(x)
f(x)
Stretches f(x) vertically with scale factor 2

12. Simple transformations
The diagram shows a sketch of the curve f(x) = 2x which passes through the point A(0,1).
Sketch:
g(x) = f(2x)
f(x) = 22x
f(2x)
f(x)
Stretches f(x) horizontally with scale factor 1 2