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Good job, Group 4!

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Very detailed, good job you're so talented

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Shows large increases/decreases in values because of a change in the value of x (exponent)

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Shows large increases/decreases in values because of a change in the value of x (exponent)

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

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

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y = 10^x and y = log of x to the base 10 are inverses

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y = 10^x and y = log of x to the base 10 are inverses

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- Looking at the graph, log of x to the base 10 is a reflection of 10^x
- Reflection on the graph h : y = x

Jamin E.

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You're doing a great job here, Group 4! Keep it up! :)

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- A logarithmic function will have the domain as (0, ∞).
- The range of a logarithmic function is (−∞, ∞).
- The logarithmic function graph passes through the point (1, 0).
- The graph of a logarithmic function has a vertical asymptote at x = 0.
- Bianca A.

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- Both the square root and logarithmic functions have a domain limited to x values greater than 0
- The range of the square root function is all non-negative real numbers.
- The range of the logarithmic function is all real numbers.

- Rocio T.

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e^x and ln(x) are inverses of each other

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e^x and ln(x) are inverses of each other

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Looking at the functions, they mirror one another across the line y = x

Thea R.

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

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

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The function y=b^x only takes on positive values, or outputs, because the x-axis is the horizontal asymptote.
Jamin E.

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If the base, b, is greater than
1, then the function increases exponentially at a growth rate of b. This is known as exponential growth.

If the base, b, is less than 1 (but greater than 0) the function decreases exponentially at a rate of b. This is known as exponential decay.

- Bianca A.

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- they are inverses of each other
- exponential function can be seen as ƒ(x) = ex
- logarithmic function is seen as g(x) = ln x

- Rocio T.

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The graph passes through the point (0,1)

The domain is all real numbers.

The range is y>0.

The graph is increasing.

The graph is asymptotic to the x-axis as x approaches negative infinity.

- Bianca A.

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

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The graphs of y = a raised to 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.