7.7.1: Transform exponential and logarithmic functions by changing

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LEARNING GOALS LESSON 7.7
7.7.1 Transform exponential and logarithmic
functions by changing
parameters. 7.7.2 Describe the effects of
changes in the coefficients of
exponents and logarithmic functions.
TRANSFORMING EXPONNTIAL FUNCTIONS Translation
Rule Example 1 Vertical Translation
f(x) k 3 units up g(x) 2x3 6 units
down Horizontal Translation f(x-h) 3
units right g(x) 2x 3 1 unit
left Vertical Stretch/Comp. af(x) stretch
by 6 g(x) 6(2x) comp. by ¼ Horiz.
Stretch/Comp. stretch by 5 compress by
? Reflection (x-axis) -f(x) x-axis reflection
g(x) -2x (y-axis) f(-x) y-axis reflection
g(x) 2-x
Example 1 Translating Exponential Functions
g(x) 2x 1. Tell how the graph is transformed
from the graph of the function f(x) 2x.
The asymptote is y _____. The transformation
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Check It Out! Example 1
f(x) 2x 2. Describe the asymptote. Tell how
the graph is transformed from the graph of the
function f(x) 2x.
The asymptote is y ____. The transformation
moves the graph
Example 2 Stretching, Compressing, and
Reflecting Exponential Functions
Describe how the graph is transformed from the
graph of its parent function.
A. g(x) ?(1.5x)
y-intercept
parent function f(x)
asymptote y
B. h(x) ex 1
parent function f(x) ex
y-intercept e
asymptote y
CAUTION! Really is h(x) e(-(x-1)) DISTRIBUTE!
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Check It Out! Example 2b
g(x) 2(2x)
g
f
parent function f(x)
y-intercept
asymptote y
TRANSFORMING LOGARITHMIC FUNCTIONS Translation
Rule Example Vertical Translation
f(x) k 3 units up g(x) log(x)3
6 units down Horizontal Translation
f(x-h) 2 units right g(x) log(x-2) 1 unit
left Vertical Stretch/Comp. af(x) stretch
by 6 g(x) 6log(x) comp. by ¼ Horiz.
Stretch/Comp. stretch by 5 g(x) log(?x)
compress by ? Reflection (x-axis)
-f(x) x-axis reflection g(x) -log(x)
(y-axis) f(-x) y-axis reflection g(x) log (-x)
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Example 3A Transforming Logarithmic Functions
Find the asymptote. Describe how the graph is
transformed from the graph of its parent function.
g(x) 5 log x 2
asymptote x
Example 3B Transforming Logarithmic Functions
Find the asymptote. Describe how the graph is
transformed from the graph of its parent function.
h(x) ln(x 2)
asymptote x
CAUTION! Really is h(x) ln(-(x-2)) DISTRIBUTE
!
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Example 4A Writing Transformed Functions
Write each transformed function.

1. f(x) 4x is reflected across both axes and move
   units down.

B. f(x) ln x is compressed horizontally by a
factor of ½ and moved 3 units left.
CAUTION! Be sure to apply horizontal stretches
and compressions last (enabling you to
distribute!)
C. f(x) log x is translated 3 units left and
stretched vertically by a factor of 2.