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Good job, Group 1!

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the horizontal asymptote of y=b^x will always be the x-axis

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the horizontal asymptote of y=b^x will always be the x-axis

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any positive value will only result to a positive value when raised to any power

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y=a^x will be a reflection and is an inverse of y=log of x to the base a

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You're doing a great job here, Group 1! Keep it up! :) 

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You're doing a great job here, Group 1! Keep it up! :) 

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The domain of the function is all positive numbers. That means that that value of the function will always be positive.

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The domain of the function is all positive numbers. That means that that value of the function will always be positive.

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This is because

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(0,1) will always be a point on a exponential function in the form of y = b^x

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(0,1) will always be a point on a exponential function in the form of y = b^x

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because b is positive, it will result to 1 when it is raised to 1

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Difference Between logarithmic and Square-root functions

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Difference Between logarithmic and Square-root functions

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When graphed, the logarithmic function is similar in shape to square root functions, but has a vertical asymptote when
x approaches 0 from the right.

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(0,1) will always be a point on a exponential function in the form of y = b^x

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(0,1) will always be a point on a exponential function in the form of y = b^x

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because b is positive, any number raised to 0 will result to 1

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The rate at which an exponential graph increases/decreases changes as x increases (or decreases)

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The graphs of y=e^x and y=ln(x) are reflections of each other. They reflect on opposite sides of y=x.

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The graphs of y=10^x and y=log(x) are reflections of each other.  They reflect on opposite sides of y=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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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.