1. TRANSFORMING EXPONNTIAL FUNCTIONS
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) = 2x+3
6 units down:
Horizontal Translation: f(x-h) 3 units right: g(x) = 2x – 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 ⅓:
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) = 2–x + 1. Tell how the graph is transformed from the graph of the function f(x) = 2x.
The asymptote is y = _____.
The transformation:

2. The asymptote is y = ____. The transformation moves the graph:
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) = ⅔(1.5x)
y-intercept:
parent function: f(x) =
asymptote: y =
B. h(x) = e–x + 1
parent function: f(x) = ex
y-intercept: e
asymptote: y =
CAUTION!
Really is:
h(x) = e(-(x-1))
DISTRIBUTE!

3. TRANSFORMING LOGARITHMIC FUNCTIONS:
Check It Out! Example 2b
g(x) = 2(2–x) 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(⅕x)
compress by ⅓:
Reflection: (x-axis) -f(x) x-axis reflection: g(x) = -log(x)
(y-axis) f(-x) y-axis reflection: g(x) = log (-x)

4. CAUTION! Really is: h(x) = ln(-(x-2)) DISTRIBUTE!
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!

5. Example 4A: Writing Transformed Functions
Write each transformed function.
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.