3.3 graphs of exponential functions
Transcript of 3.3 graphs of exponential functions
3.3 Graphs of Exponential Functions
Exponential Growth Graphs•When b > 1 ▫ graph moves away from x-axis quickly from left to right.
•y-intercept is at point (0, a).
Exponential Decay Graphs•When 0< b < 1 ▫ graph moves towards x-axis quickly from left to right.
•y-intercept is at point (0, a).
Asymptotes•An asymptote is a line that a graph approaches (but does not touch) as it moves away from the origin.
•Functions of the formy = a(b)x have horizontal asymptotes at y = 0.
Domain & Range•Domain & Range describe which input/output values will work for a given function.•Domain – set of all input values (x’s)▫Look left and right•Range – set of all output values (y’s)▫Look up and down•Can be written using inequalities.
Example 1:•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
Example 2:•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
You Try!•Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:
Graphing Exponential Functions•To graph y = a(b)x 1. Make a table2. Plot the points3. Connect with a smooth curve
Be Careful:• Don’t cross the asymptote (y = 0)!!• Check that y-int is (0, a)!!
Example 1:•Graph •State the domain and range.
Example 2:•Graph •State the domain and range.
You Try!
•Graph •State the domain and range.
Example 3:•Graph •State the domain and range.
Example 4:•Graph •State the domain and range.
You Try!•Graph •State the domain and range.
Transformations •Remember: •+ and – mean shift•Changing the input shifts left/right▫Do the opposite!!•Changing the output shifts up/down
•We will call the original function y = a(b)x the “parent function”•Its graph is the “parent graph”
Example 1:•Identify the parent function and describe the transformation on it.
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2.
3.
You Try!•Identify the parent function and describe the transformation on it.
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3.
To Graph:•Sketch the parent graph with a dashed line.•Shift points and draw final graph. •Example:•Graph •Domain:•Range:
Example 2:
•Graph
•Domain:•Range:
You Try!
•Graph
•Domain: •Range: