1. Section 6.4 – Graphs of Logarithmic Functions

2. Dom: Range:
The point (0, 1) is on the graph.
𝑦=0 is a horizontal asymptote
Dom: Range:
The point (1, 0) is on the graph.
𝑥=0 is a vertical asymptote

3. Graph the function and its inverse on the same set of axes.

4. Describe the transformations of the basic graph 𝑓 𝑥 = log 3 𝑥 and graph the function.
Shift the graph of 𝑓 𝑥 = log 3 𝑥 to the right 2 units
Domain:
Range:
Vertical Asymptote:
𝑥−2>0
𝑥>2
(2, ∞)
(−∞, ∞)
𝑥=2

5. Describe the transformations of the basic graph 𝑓 𝑥 = 𝑙𝑜𝑔 𝑥 and graph the function.
Shift the graph of 𝑓 𝑥 = log 𝑥 down 5 units
Domain:
Range:
Vertical Asymptote:
𝑥>0
(0, ∞)
(−∞, ∞)
𝑥=0

6. 𝑓 𝑥 = 2 𝑥 𝑓 𝑥 = 𝑒 𝑥 𝑓 𝑥 = 5 𝑥 𝑓 𝑥 = 10 𝑥 𝑓 𝑥 = 2 𝑥 𝑓 𝑥 = 𝑒 𝑥 𝑓 𝑥 = 5 𝑥
𝑓 𝑥 = 2 𝑥
𝑓 𝑥 = 𝑒 𝑥
𝑓 𝑥 = 5 𝑥
𝑓 𝑥 = 10 𝑥
𝑓 𝑥 = 2 𝑥
𝑓 𝑥 = 𝑒 𝑥
𝑓 𝑥 = 5 𝑥
𝑓 𝑥 = 10 𝑥
𝑓 𝑥 = log 2 𝑥
𝑓 𝑥 = ln 𝑥
𝑓 𝑥 = log 5 𝑥
𝑓 𝑥 = log 𝑥
𝑓 𝑥 = log 2 𝑥
𝑓 𝑥 = ln 𝑥
𝑓 𝑥 = log 5 𝑥
𝑓 𝑥 = log 𝑥
The larger the base, the more slowly the function increases (the closer it is to the 𝑥-axis).

7. Describe the transformations of the basic graph 𝑓 𝑥 = ln 𝑥 and graph the function.
Shift the graph of 𝑓 𝑥 = ln 𝑥 Right 3 units
Flip over 𝑥-axis
Up 2 units
Domain:
Range:
Vertical Asymptote:
𝑥−3>0
𝑥>3
(3, ∞)
(−∞, ∞)
𝑥=3

8. Determine the domain/range and vertical asymptote of the logarithmic function.
12−3𝑥>0
12>3𝑥
𝑥<4
(−∞,4)
(−∞, ∞)
𝑥=4
p. 513: 3 – 15 odd, 26 – 33 all, 38 – 40 all