Logarithmic functions are inverses of exponential functions of the form f(x)=a^x. They can be graphed using mirroring and rotational methods. A logarithmic function is of the form f(x)=loga(x) where x>0, a>0, and a is not equal to 1. Key properties of logarithmic functions include their domain and range, extrema, asymptotes, whether they are increasing or decreasing, and end behavior.

1. Analyzing logarithmic functions

2. A logarithmic function is the inverse of an exponential function(f(x)= a X b^x). We can find the graph by mirror and rotational methods. The inverse f(x)= a^x is f^-1(x)= log a X, where x>0, a>0, and a can't = 1. What is a logarithmic function?

4. Range- range is all the y- values.

5. Extrema- extrema is known as maxima or minima. Focusing on the largest and smallest value.

6. Asymptotes- an asymptote is a line that a graph approaches, but doesn't intersect.

13. Range: (-infinity, infinity)

14. Continuity: Continuous

15. Symmetry, Boundedness, Extrema: None

16. Asymptotes: x= o

17. Increasing/ Decreasing: increasing

18. End Behavior: lim f(x)= infinity lim f(x)= - infinity

19. x >>infinity x>>zero

21. Range:(-infinity, infinity)

22. Continuity: continuous

23. Symmetry, Boundedness, Extrema: none

24. Asymptotes: x= 0

25. Increasing/ Decreasing: increasing

26. End Behavior: lim f(x)= infinity lim f(x)= - infinity

27. x>>infinity x>>zero