To complete this page, you’ll need to open Modeling Covid Spread (Desmos). The curve you’ll see is the graph of ℎ(𝑥) = 2𝑥.
Another, curve 𝑓(𝑥) is hiding behind it. For starters, the values of the coefficients of 𝑓(𝑥) have been set to make it equivalent to ℎ(𝑥).
Base 𝑏
1 Set 𝑘 back to 0, then try different values of 𝑏. For what values is the function undefined (the line disappears)?
2 Keeping 𝑎=1 and 𝑘=0, change math{b} to 0.5, 1, and 2, graphing each curve below. For each curve, label the coordinates at x=1, 2, and 3.
𝑏=0.5 |
𝑏=1 |
𝑏=2 |
3 What does 𝑏 tell us about an exponential function, when 𝑏 is greater than 1?
4 What does 𝑏 tell us about an exponential function, when 𝑏 is less than 1?
Vertical Shift…and Horizontal Asymptote 𝑘
5 Keeping 𝑎=1 and 𝑘=0, try changing the value of 𝑘 to -10, 0, and 10, graphing each curve in the squares below. For each curve, find and label the y-value where the curve is "most horizontal", then draw a horizontal line at that y-value.
𝑘=−10 |
𝑘=0 |
𝑘=10 |
6 What does 𝑘 tell us about an exponential function?
Initial Value 𝑎
7 Set 𝑘=0 and 𝑏=2. Change the value of 𝑎 to 10, 2, and -5, graphing each curve in the squares below. For each curve, label the y-intercept (x=0).
𝑎=10 |
𝑎=2 |
𝑎=−5 |
8 What does 𝑎 tell us about an exponential function?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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