Unit 5: Logarithmic Functions Flashcards
Composite Functions can be written as…
What happens to the x and y values for inverses of functions?
The x and y of the original function flip for the inverse
What line does the original graph reflect over to get the inverse graph?
The line y=x
Two functions are inverses if and only if…
The domain of the inverse of f is…
The range of f
The range of the inverse of f is…
The domain of f
Finding inverse functions of rational functions
- Switch the x and y values
- Multiply/Distribute both sides by the denominator
- Move all terms that have y to the left side of the equals and move all terms that do not have y to the right side of the equals
- Factor out a y from the terms on the left side
- Divide both sides by the terms remaining
- Rewrite the equation with proper inverse notation
The inverse of an exponential function is…
a logarithmic function
To switch from an exponential scatter plot to a logarithmic scatter plot…
take the log of all the y-values and replot using 10^n as your tick marks for your y-axis.
How do exponential functions change?
Over equal x intervals, the y values change multiplicatively
How do logarithmic functions change?
Over equal y intervals, the x values change multiplicatively
Basic exponential function
Basic logarithmic function
Log graph where a>0 and b>1
Log graph where ‘a’ is less than 0 and b>1
End behavior statements for logarithmic functions
Product Property for Logs
Quotient Property for Logs
Power Property for Logs
Change of Base Property
