1. Graphs of Logarithmic Functions
One more fun day in Section 3.3b

2. Let’s start with Analysis of the Natural Logarithmic Function:
The graph:
Domain:
Range:
Continuous on
Increasing on
No Symmetry
Unbounded
No Local Extrema
No Horizontal Asymptotes
Vertical Asymptote:
End Behavior:

3. Note: Any other logarithmic function
The “Do Now”  Analysis of the Natural Logarithmic Function
The graph:
Note: Any other logarithmic
function
with b > 1 has the same domain,
range, continuity, inc. behavior,
lack of symmetry, and other
general behavior of the natural
logarithmic function!!!

4. Reflect across the y-axis, Trans. right 3  The graph?
Describe how to transform the graph of y = ln(x) or y = log(x)
into the graph of the given function. Sketch the graph by hand
and support your answer with a grapher. 1.
Trans. left 2  The graph? 2.
Reflect across the y-axis,
Trans. right 3  The graph?

5. Vert. stretch by 3  The graph?
Describe how to transform the graph of y = ln(x) or y = log(x)
into the graph of the given function. Sketch the graph by hand
and support your answer with a grapher. 3.
Vert. stretch by 3  The graph? 4.
Trans. up 1  The graph?

6. Trans. right 1, Horizon. shrink by 1/2,
Describe how to transform the graph of y = ln(x) or y = log(x)
into the graph of the given function. Sketch the graph by hand
and support your answer with a grapher. 5.
Trans. right 1, Horizon. shrink by 1/2,
Reflect across both axes, Vert. stretch by 2,
Trans. up 3  The graph???

7. 1. Graph the given function, then analyze it for domain, range,
continuity, increasing or decreasing behavior, boundedness,
extrema, symmetry, asymptotes, and end behavior. 1. D: R:
Continuous
Dec:
No Symmetry
Unbounded
No Local Extrema
Asy:
E.B.:

8. 2. Graph the given function, then analyze it for domain, range,
continuity, increasing or decreasing behavior, boundedness,
extrema, symmetry, asymptotes, and end behavior. 2. D: R:
Continuous
Dec:
No Symmetry
Unbounded
No Local Extrema
Asy:
E.B.: