Exponential and Logarithmic Functions Recap

Hello. Here’s a quick re-cap of what we have learned about exponential and logarithm functions before winter break.

Graphing Exponential Functions

Key points to remember:

•   Basic curve: y=c^x
• The same transformation rules apply:

 y=(a)c^b(x-h)+k 

o   a – vertical stretch by a factor of lal about the x axis.

-          ex: y= (5)c^x (Vertical stretch by a factor of 5 about the x axis.)

o   b – horizontal stretch by a factor of 1/b about the y axis.

-          ex. y=c^2x (Horizontal stretch by a factor of ½ about the y axis.)

o   h – horizontal translation

-          ex. y=c^(x+2) (Horizontal translation by 2 units to the left)

o   k – vertical translation

-          ex. y=c + 3 (Vertical translation by 3 units up)

 

Steps:

1.  Determine the horizontal asymptote. (The horizontal asymptote is related to the vertical translation, k.)
2.  Table of Values; pick x values.
3.   Plug in the x values into the equation in order to find the corresponding y values.
4.  Graph.

y = 2^z

HA @ y=0

Table of Values:

         

Graph:

Graphing Logarithmic Functions

Key points to remember:

•   A logarithm function is the inverse of an exponential function.

Steps

1.  Convert logarithmic function to exponential function using the 7 Rule.
2.   Determine the vertical asymptote.
3. Table of Values; pick y values.
4. Plug in the y values into the equation in order to find the corresponding x values.
5.  Graph.

f(x) = log₂x -> 2^y = x

VA @ x=0

Table of Values

          

Graph:

Expanding and Simplifying Logarithmic Expressions

Key points to remember when expanding:

•   Roots -> fraction exponent
•  Division -> subtraction
•  Multiplication -> addition
•  Exponent -> coefficient

Ex.

 

Key points to remember when simplifying:

•  Move all negative terms to the end
• Coefficient -> exponent
•  Addition -> multiplication
•  Subtraction -> division
•  Fraction exponent -> roots