Unit 3 Logarithmic and Exponential Functions

Logarithmic Functions

100

What is a logarith function 

logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as

For x > 0 , a > 0, and a

200

What is the equation for a logarithmic function 

Log_bX=y

300

What is the base in this equation? log₂x=4

Base=2

400

What is the change of base formula

Log_ba=Log_za/Log_zb (this is a fraction btw)

Exponential Functions

100

What is a Exponential Functions

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e

200

What is the equation for a logarithmic function

B^y=x

300

What is the base in this equation? 5^y=x 

Base=5

400

What is the domain and range of y=2^x

Domain:(-∞,∞)

Range:(0,∞)

Graphing

100

When graphing an exponential function in the form f(x)=b^x what is the horizontal asymptote on 

Asymptote=0

200

What is happening to the original graph after the Tranformation?                           f(x)=b^x  —> g(x)=-b^x

 

It is reflecting it

300

When graphing the inverse what happens to the coordinates?

Everything Flip Flops

400

What happens to the original graph after the transformation? F(x)=log₂6 —> g(x)=log₂(-6)+12

Vertical translation and reflection 

Log->ExpExp->Log

100

What way do you make a Logarithmic Function into an Exponential Function, and how do you make an Exponential function into a Logarithmic Function? 

Using the e method for log—>exp and the L method for exp—>log 

200

What is this logarithmic equation in exponential form

log₂x=4

2⁴=x

300

What is this exponential function as a Logarithmic function

3^x=9  

Log₃9=x

400

Evaluate this equation. 

Log₃81

3^x=81 x=4