Print this Page
9.4 – Graphs of Exponential Functions
Key Terms
 Horizontal Asymptote – A horizontal line that the graph of a function approaches but never intersects.
 A function has a horizontal asymptote at every yvalue where it is undefined and near which the function’s values become very large positive or negative numbers.
 Think of an asymptote like an electric fence. You can’t cross it! You can’t even touch it!
 Range – The set of a function’s output values (yvalues).
 yintercept – A point where the graph of a function crosses the yaxis.
 A function has at most one yintercept.
 The yintercept of the line with the equation y = mx + b is the point (0, b).
Review
Graph Behavior 
 Increasing graphs slant or curve up from left to right
 Decreasing graphs slant or curve down from left to right
 All exponential graphs are curved, not straight.

Notes
The Exponential Function’s Base 
 The value of the base determines whether the graph increases or decreases from left to right.
 The base for an exponential function can never be a negative number.
 A negative value of b would make the function undefined for many values of x.

 If b > 1, then the graph increases

 If 0 < b < 1, then the graph decreases

Domain and Range 
 The domain of a function is all the input values it will accept.
 Domain ends with in for input.

 The range of a function is all the output values it will return.
 Range starts with r for return.
 For , the ranges is all positive real numbers greater than a.

Vertical Translations (Shifting Up and Down) 
 Shifting affects the range, but not the domain.
 The domain is always “All real numbers.”
 Range will always be greater than the shift.
 The range of the top graph is y > 5
 The range of the bottom graph is y > 3

Vertical Stretching and Compressing 
 Multiplying a function by a negative number flips the graph across the xaxis.
 When the function is flipped across the xaxis, the inequality sign of the range is reversed.

 To horizontally stretch an exponential function, you multiply the input variable by a number between zero and 1 (a positive fraction).
 To horizontally compress it, you multiply the input variable by a number greater than 1.

Translations (All Together) 

Exponential Functions and Graphs: Chart 

Examples
Important!
Practice (Apex Study 9.4)
 Try practice problems on Pgs 14, 17, 18
 Mandatory: write and answer problems on Pg 22
 1 Quiz
Permanent link to this article: http://newvillagegirlsacademy.org/math/?page_id=4725