1. EXPONENTIAL FUNCTION where (base) b > 0 and b For 0 < b < 1,
The graph is increasing and asymptotic to (-) x-axis.
The graph is decreasing and asymptotic to (+) x-axis.
(0 , 1) is always a point on the graph
(0 , 1)
(0 , 1) 1

2. x -2 -1 1 2 f(x) 4 x -2 -1 1 2 f(x) 4 (0 , 1) (-2 , 4) (2 , 4)1 2
f(x) 4 x -2 -1 1 2
f(x) 4
(-2 , 4)
(2 , 4)
(-1 , 2)
(1 , 2)
(0 , 1)
(0 , 1) 2

3. x -2 -1 1 2 f(x) x -2 -1 1 2 f(x) 4 (0 , -2) (-2 , 2) (-2 , 4)1 2
f(x) x -2 -1 1 2
f(x) 4
(-2 , 2)
(-2 , 4)
(-1 , 0)
(-1 , 2)
(0 , -2)
(0 , 1) 3

4. x 1 2 3 4 f(x) x -2 -1 1 2 f(x) 4 (-2 , 4) (-1 , 2) (0 , 1) (0 , 4)1 2 3 4
f(x) x -2 -1 1 2
f(x) 4
(-2 , 4)
(0 , 4)
(1 , 2)
(-1 , 2)
(2 , 1)
(0 , 1) 4

5. x -2 -1 1 2 f(x) 4 x -2 -1 1 2 f(x) 3 4 6 (0 , 1) (2 , 4) (1 , 2)1 2
f(x) 4 x -2 -1 1 2
f(x) 3 4 6
(2 , 6)
(2 , 4)
(1 , 4)
(0 , 3)
(1 , 2)
(0 , 1) 5

6. x -2 -1 1 2 f(x) 4 x -4 -3 -2 -1 f(x) 1 2 4 (0 , 1) (2 , 4) (1 , 2)1 2
f(x) 4 x -4 -3 -2 -1
f(x) 1 2 4
(2 , 4)
(0 , 4)
(1 , 2)
(-1 , 2)
(0 , 1)
(-2, 1) 6

7. x -1 1
f (x) e x -1 1
f (x) e
(-1 , e)
(1 , e)
(0 , 1)
(0 , 1) 7

8. Rules of Exponents

9. Logarithm of a number N to a positive base b ( ) is the exponent to which b must be raised in order to get N.
S.Y.Tan

10. Properties of Logarithm or Laws of Logarithm
S.Y.Tan

11. LOGARITHMIC FUNCTION for (base) b > 0 and b
logarithmic form exponential form
Change logarithmic form to exponential form
b = e (natural logarithm)
b =10 (common logarithm) 11

12. LOGARITHMIC FUNCTION for (base) b > 0 and b
logarithmic form exponential form
Change logarithmic form to exponential form 12

13. LOGARITHMIC FUNCTION for (base) b > 0 and b
logarithmic form exponential form
Change exponential form to logarithmic form 13

14. LOGARITHMIC FUNCTION for (base) b > 0 and b
logarithmic form exponential form
Change exponential form to logarithmic form 14

15. Use the properties of logarithm to expand each expression.
The properties of logarithms are useful for rewriting logarithmic expressions in forms that simplify the operations of algebra.
Use the properties of logarithm to expand each expression. 15

16. Use the properties of logarithm to condense the expression as single logarithm.16

17. Evaluate the following.17

18. Logarithmic function and Exponential function are inverse functions of one another.18

19. Logarithmic function and Exponential function are inverse functions of one another.19

20. The graph is decreasing and asymptotic to (+) y-axis.
For 0 < b < 1,
For b > 1,
The graph is decreasing and asymptotic to (+) y-axis.
The graph is increasing and asymptotic to (-) y-axis.
(1 , 0) is always a point on the graph
(1, 0)
(1 , 0) 20

21. (2, 4)
(0, 1)
(4, 2)
(1 , 0) 21

22. (-1, 2)
(0, 1)
(1 , 0)
(2, -1) 22

23. (1, e)
(0, 1)
(e, 1)
(1 , 0) 23

24. Solve for x in terms of y 24

25. x = -1
y = x
y = -1

26. Solve for x in terms of y 26

27. y = x
y = 2
x = 2

28. Solve for x in terms of y 28

29. x = 0
y = 0

30. Exponential and Logarithmic Equations30

31. Exponential and Logarithmic Equations31

32. Exponential and Logarithmic Equations32

33. Exponential and Logarithmic Equations
Check if part
of domain
Check if part
of domain 33

34. Exponential and Logarithmic Equations
Base should always be positive
Check if part
of domain 34

35. Exponential and Logarithmic Equations
Check if part
of domain
Check if part
of domain 35

36. Exponential and Logarithmic Equations
Check if part
of domain 36

37. Exponential and Logarithmic Equations
Check if part
of domain 37

38. Exponential and Logarithmic Inequalities38

39. Exponential and Logarithmic Inequalities39

40. Exponential and Logarithmic Inequalities
1/2 3 40

41. Exponential and Logarithmic Inequalities41

42. Zeros: x = 4 x = -6 Interval -6 3 4 -6 3 4 -6 S.Y.Tan
Signs change before and after zeros
Interval 3 -6 3 4 -6
S.Y.Tan

43. Exponential and Logarithmic Inequalities43

44. Zeros: x = 5/8 x = -2 Interval -2 1/3 5/8 -2 1/3 5/8 -2 S.Y.Tan
Signs change before and after zeros
Interval
1/3 -2
1/3
5/8 -2
S.Y.Tan