3.3 Logarithmic Graphs Exploration
Task #1
1. Fill in the table of values for y = log x and plot them/graph it by hand.
x
y
1
10
1
10
2. Fill in the table of values and graph y = 10x on the same coordinate plane.
x
y
1
2
-1
-2
Task #2
1. Fill in the table of values for y = ln x and plot them/graph it by hand.
x
y
e (≈2.718)
e2 (≈7.389)
e3 (≈20.086)
2. Fill in the table of values and graph y = ex on the same coordinate plane.
x
y
1
2
-1
-2
Task #3
Find each of the following for y = log x and y = ln x.
1. Domain
2. Range
3. Increasing/Decreasing
4. Bounded
5. Vertical Asymptote
6. Horizontal Asymptote
7. Continuity
8. End Behavior
Task #4
1. log(10x) = ______
10 logx = ______
2. What does this tell us?
3. ln (ex) = ______
e lnx = ______
4. What does this tell us?
Task #5
1. Describe the transformation from f(x) to g(x) for each without a calculator – just using
what you know about the general transformation rules.
2. Then, check your answer by graphing the function on your graphing calculator. Sketch a
graph of each on your paper.
a) f(x) = log(x)
b) f(x) = log(x)
c) f(x) = ln(x)
d) f(x) = ln(x)
g(x) = log(x + 1)
g(x) = -log(x – 3)
g(x) = ln(x) + 3
g(x) = ln(-x) + 2