Transcript Graphs of Logarithmic Functions

Graphs of
Logarithmic
Functions
One more fun day in Section 3.3b
Let’s start with Analysis of the Natural Logarithmic Function:
The graph:
f  x   ln x
 0, Range:  , 
Continuous on  0,
Increasing on  0,
Domain:
No Symmetry
Unbounded
No Local Extrema
No Horizontal Asymptotes
Vertical Asymptote:
End Behavior:
x0
lim  ln x   
x 
The “Do Now”  Analysis of the Natural Logarithmic Function
The graph:
f  x   ln x
Note: Any other logarithmic
function
g  x   logb x
with b > 1 has the same domain,
range, continuity, inc. behavior,
lack of symmetry, and other
general behavior of the natural
logarithmic function!!!
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.
g  x   ln  x  2
Trans. left 2  The graph?
2. h x  ln 3  x  ln  
 



Reflect across the y-axis,
Trans. right 3  The graph?
 x  3
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.
g  x   3log x
Vert. stretch by 3  The graph?
4.
h  x   1  log x
Trans. up 1  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.
5.
g  x   2ln  2  2x   3
 2 ln  2  x  1   3
Trans. right 1, Horizon. shrink by 1/2,
Reflect across both axes, Vert. stretch by 2,
Trans. up 3  The graph???
Graph the given function, then analyze it for domain, range,
continuity, increasing or decreasing behavior, boundedness,
extrema, symmetry, asymptotes, and end behavior.
1.
f  x    log  x  2
Continuous
 , 
Dec:  2, 
No Symmetry
Unbounded
D:
Asy:
 2, 
x  2
R:
E.B.:
No Local Extrema
lim f  x   
x 
Graph the given function, then analyze it for domain, range,
continuity, increasing or decreasing behavior, boundedness,
extrema, symmetry, asymptotes, and end behavior.
2.
f  x   5ln  2  x   3
Continuous
 , 
Dec:  ,2
No Symmetry
Unbounded
D:
Asy:
 ,2
x2
R:
E.B.:
No Local Extrema
lim f  x   
x 