3.1 Exponential Functions and Their Graphs

Properties of Exponents:

When you multiply two terms, you add the exponents

When you divide two terms, you subtract the exponents

When you raise a power to a power, you multiply the exponents

When you raise a term to zero, it equals 1

Exponents to the power of n:

Definition of Exponential Function: 

Properties of an exponential function: 

Domain: 

Range: 

x-intercept: none

y-intercept: (0,1)

Horizontal Asymptote: 

Vertical Asymptote: none

Example:   

In the function above, the graph approaches the line y=0 and intersects the y-axis at (0,1).  

Shifting, Reflecting, and Stretching Exponential Functions

• a represents a vertical stretch or compress, if a is negative, the graph reflects in the x-axis
• b will make the graph's rate increase faster or slower
• c will shift the graph left or right
• d will shift the graph up or down

One-to-One Property

If the equation has the same base on both sides, the exponents can be set equal to each other and solved for x.

Example:

125 can be rewritten so it has the equation has a base of 5 on the right and left side.

Since both sides have a base of 5, the exponents can be set equal to each other to solve for x.