To complete this page, you’ll need to open Exploring Logarithmic Functions (Desmos). The red curve is the graph of ℎ(𝑥) = 1 log2 𝑥 + 0. It has 𝑎=1, 𝑏=2, and 𝑐=0. You can modify the curve 𝑔(𝑥) (behind ℎ, shown in blue) by changing its 𝑎, 𝑏, and 𝑐.
Base 𝑏
Set 𝑐 to zero and 𝑎 to one.
1 Change the value of 𝑏 to 3, 5, and 10, graphing each curve below. In each graph, label the coordinate where 𝑥=1, and also where y=1, 2, and 3.
𝑏=2 |
𝑏=3 |
𝑏=10 |
2 How does the value of 𝑏 impact a logarithmic function?
3 What connections can you draw between the value of 𝑏 and exponents?
Vertical Shift 𝑐
4 Try changing the value of 𝑐 to -10, 0, and 10, graphing each curve below. In each graph, label the coordinate where 𝑥=1.
𝑐=−10 |
𝑐=0 |
𝑐=10 |
5 How does the value of 𝑐 impact a logarithmic function?
6 Why does 𝑦 = 𝑐 when 𝑥=0?
Logarithmic Coefficient 𝑎
7 Set c to zero and b to ten, then zoom out so you can see as far as 𝑥 = 1,000,000
Change the value of 𝑎 to 1, 2, and 3, graphing each curve below. In each graph, label the coordinates where x=10, 100, and 1000.
𝑎=−2 |
𝑎=0 |
𝑎=2 |
8 What is the value of 𝑥 when log10(𝑥) = 6? What about when 2 log10(𝑥) = 6? When 3 log10(𝑥) = 6?
★ How are 𝑎 and 𝑏 related?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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