April 13, 2016
Warmup
1.)
7.3 Logarithmic Functions as Inverses
Which function best represents this graph?
(This a transformation
of the parent function
.)
2.) Write each equation in logarithmic form.
3.) Write each equation in exponential form.
4.) Evaluate each logarithm.
D
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April 13, 2016
Find the inverse of each function:
Remember:
To find an inverse algebraically,
you switch x and y first,
then solve for y .
You can rewrite the log as an
exponential function first, if
you refer.)
The inverse of an exponential
function is a logarithmic function.
April 13, 2016
April 13, 2016
Find the inverse of each function:
5.) y = log 5 x
The inverse of a logarithmic
function is an exponential
function.
6.) y = log (x + 2)
Remember:
To find an inverse algebraically,
you must switch x and y first,
then solve for y .
You can rewrite the log as an
exponential function first, if
you refer.)
7.) y = log 5 (5x)
8.) y = log 3 (x+ 1)
April 13, 2016
Graphing inverse functions
9.) Graph
and its inverse function.
none
x-intercept: ­­­­­­­­_________________
(0,1)
y-intercept:__________________
H.A.: y=0
Asymptote: ­­________________
x= all real numbers
Domain: ­­­­­­­­­___________________
y>0
Range:___________________
Inverse Function: ____________________
(1,0)
x-intercept: ­­­­­­­­_________________
none
y-intercept:__________________
V.A.: x=0
Asymptote: ­­________________
x>0
Domain: ­­­­­­­­­___________________
y= all real numbers
Range:___________________
Recall that the graphs of inverse
functions are reflections of each
other across the line y = x.
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April 13, 2016
Find the x-intercept of the function.
(Hint: set the equation =0)
Find the asymptotes without graphing.
April 13, 2016
16.) Graph of y = log 4 (x-3) + 4 and the parent function.
Parent function:________________________
(1,0)
x-intercept: ­­­­­­­­_________________
none
y-intercept:__________________
V.A.: x=0
Asymptote: ­­________________
y=no solution
x>0
Domain: ­­­­­­­­­___________________
y=all real numbers
Range:___________________
y = log 4 (x-3) + 4
right 3 , up 4
Transformations:__________________
x-intercept: ­­­­­­­­_________________
none
y-intercept:__________________
V.A.: x=3
Asymptote: ­­________________
x>3
Domain: ­­­­­­­­­___________________
y=all real numbers
Range:___________________
April 13, 2016
HW p. 456; 36-39, 61 - 67 odd 73,75,92-95
April 13, 2016
HW p. 456; 36-39, 61 - 67 odd 73,75,92-95
April 13, 2016