You’ll need to have Fitting Wealth-v-Health and Exploring Logarithmic Models (Desmos) open to Slide 4: Exploring Logarithmic Functions.

The curve you’ll see is the graph of r(x), an logarithmic function. Another, identical curve s(x) is hiding behind it.
1 Use the starting values of a, b, and k to complete the following equation: r(x) = s(x) = f(x) = log coefficient log base(x) + vertical shift

Base b

Keep   k  at 0 and   a  at 1. Change the value of   b  as indicated on each grid below.

2 Sketch each graph and label the coordinates where x = 1, y = 1, y = 2 and y = 3.

b = 3

b = 5

b = 10

3 How does the value of b impact the shape of a logarithmic function?

4 What connections can you draw between the value of b and exponents?

Vertical Shift k

Set   a  to 1 and   b  to 2. Change the value of   k  as indicated on each grid below.

5 Sketch each graph and label the coordinate where x = 1.

k = - 5

k = 0

k = 5

6 How does the value of k impact the shape of a logarithmic function?

7 Why does y = k when x = 1?

Logarithmic Coefficient a

Set   k  to 0 and   b  to 10, then zoom out out so you can see as far as x = 1,000.

Change s(x) to s(x) = 1 log10 (x) + 0 so that the blue curve lands on top of the red curve.

8 In each graph, label the coordinates where x = 10 and x = 100 and x = 1000.

a = - 2

a = 0

a = 2

9 What is the value of x when 1log2(x) = 4? What about when 2 log4(x) = 4? When 3 log8(x) = 4?

★ How are a and b related?

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