Algebra 2
Name _________________________
WS 11.5: Transformations of Logarithmic Functions
Class Period _______________
Comparing Parameter Changes in Logarithmic Functions
1. Graph:
f(x) = log2x in red pen
a. How does “subtracting 3 from x” in the graph g(x)
g(x) = log2(x – 3) in black pen
compare to the graph of f(x)?
h(x) = log2(x + 5) in blue pen
b. How does “adding 5 to x” in the graph h(x)
compare to the graph of f(x)?
c. What are the domain and range of each function?
f(x):
h(x):
g(x):
2. Graph:
f(x) = log5x in red pen
g(x) = log5x+ 1 in black pen
h(x) = log5x – 4 in blue pen
d. What is the asymptote of each function?
f(x):
g(x):
h(x):
a. How does “adding 1” in the graph g(x) compare to
the graph of f(x)?
b. How does “subtracting 4” in the graph h(x)
compare to the graph of f(x)?
c. What are the domain and range of each function?
f(x):
h(x):
g(x):
3. Graph:
f(x) = log3x in red pen
g(x) = –log3x in black pen
h(x) = 3log3x in blue pen
1
j(x) = log3x in pencil
3
d. What is the asymptote of each function?
f(x):
g(x):
h(x):
a. How does “multiplying by a negative” in the graph
g(x) compare to the graph of f(x)?
b. How does “multiplying by a factor of 3” in the
graph h(x) compare to the graph of f(x)?
c. How does “multiplying by a factor of 1/3” in the
graph j(x) compare to the graph of f(x)?
c. What are the domain and range of each function?
f(x):
h(x):
g(x):
j(x):
d. What is the asymptote of each function?
f(x):
g(x):
h(x):
j(x):
Given the logarithmic function: 𝑓(𝑥) = 𝑙𝑜𝑔5 𝑥
5. Write an equation that moves f(x) right 3 units and down 4 units.
6. Write an equation that reflects f(x) across the x-axis, shifts it left 2 units, and down 1 unit.
7. Write an equation that has a vertical shrink by a factor of
1
and shifts up 5 units.
4
Describe the transformation that have occurred to the logarithmic parent graph
𝑓(𝑥) = 𝑙𝑜𝑔3 𝑥 in each of the following:
8. 𝑓(𝑥) = 2 𝑙𝑜𝑔3 𝑥 + 4
9. 𝑓(𝑥) =
1
4
𝑙𝑜𝑔3 (𝑥 − 2)
10. 𝑓(𝑥) = 𝑙𝑜𝑔3 (𝑥 + 5) − 4
Write an equation that represent the graph of f(x) = log2 (x + 3) – 5
11. translated right 4 units and up 2 units
12. reflected over the x-axis, translated left 2 units and down 3 units