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Good job, Group 3!

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If the base b is less than 1 (but greater than 0), the function decreases exponentially at a rate of b. (Exponential decay) - Noelle

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If the base b, is greater than 1, then the function increases exponentially at a growth rate of b. - Noelle

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generalization about corresponding exp and  log functions: inverses of each other

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generalization about corresponding exp and  log functions: inverses of each other

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y = a^x and log to the base a of x

- Tina R.

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You're doing a great job here, Group 3! Keep it up! :)

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similarity and difference with square root function

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similarity and difference with square root function

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logb(x) same domain with √x

but log(x) has a vertical asymptote, the y-axis
- as x gets closer to 0
- y extended to negative infinity
- so does not have a minimum y-value

√x has a minimum y-value at 0

- Tina R.

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all real numbers

- Tina R.

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all positive real numbers

- Tina R.

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x=0 or the y-axis

- Tina R.

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Red - y = x
Green - y = e^x
Blue - y = lnx

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where b is a positive real number
x-intercept at (1,0)

- Tina R.

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Decreasing line if 0 < a < 1
and increasing if a>1 - Noelle

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The x-axis is always an asymptote- Noelle

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the root of a negative number is imaginary

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Red - y = x
Green - y = 10^x
Blue - y = logx

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The graphs of y = a to the x, and y = log to the base a of x

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The graphs of y = a to the x, and y = log to the base a of x

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1.  As a group, create a mind map providing the following information:

the properties and features of graphs of exponential functions,

why b is only positive in an exponential function y = b^x,

the properties and features of graphs of logarithmic functions,

the difference between the logarithmic and square-root functions.

Click this link above to access your notes.

2.  Using GeoGebra, graph in the same grid each group of functions:

y = 10^x, y = log x and y = x,

y = e^x, y = ln x and y = x.

Upload a screenshot of your work in the provided space.

What do you notice with each pair of graphs?
What is true for the functions y = 10^x and y = log x, and y = e^x and y = ln x?
Write a generalization about y = a^x and y = log to the base a of x.