15. 4. Basic Graphs of Functions.
Sketch the graph of the following functions.
1. y = x
2. y = x 2
3. y = x 3
4. y = x 4
5. y = 1
x
6. y = x
7. y = 3 x
8. y = x
9. y = a x
10. y = log a x
viernes, 24 de agosto de 12
17. 1. Exercise.
Sketch the following functions. Find the domain, range and asymptotes (if
any).
viernes, 24 de agosto de 12
18. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a
2. f(x) - a
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
viernes, 24 de agosto de 12
19. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
viernes, 24 de agosto de 12
20. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
viernes, 24 de agosto de 12
21. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a)
5. - f(x)
6. f(-x)
viernes, 24 de agosto de 12
22. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x)
6. f(-x)
viernes, 24 de agosto de 12
23. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x) Reflected about the x-axis
6. f(-x)
viernes, 24 de agosto de 12
24. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x) Reflected about the x-axis
6. f(-x) Reflected about the y-axis
viernes, 24 de agosto de 12
25. 3. Homework 3
Blackboard -> Assignments
viernes, 24 de agosto de 12