Comparing Logarithm and Exponential Functions Graphs

Change the position of the slider in order to change the base [b][i]a[/i][/b] which is used as the base of the exponential and the logarithmic functions.
Uncheck the checkbox so the logarithmic graph is hidden and only the exponential graph is showing.
Task 1
Recall the properties of an exponential graph. Select all that apply for [math]y=a^x[/math] where [math]a>1[/math]
Now uncheck the Exponential graph and select the Logarithmic graph.
Task 2
Notice the properties of the logarithmic graph. Select all that apply for [math]y=log_ax[/math] where [math]a>1[/math]
Make both the Exponential and Logarithmic graphs visible. Locate point D on the exponential function and point B on the logarithmic function.
Task 3
What is the relationship between points D and B?
Task 4
How do the properties of the two function types relate? Select all that apply.
Task 5
How do the properties of the two function types differ? Select all that apply.
Task 6
What do you notice about the intersection between the exponential and logarithmic graphs when they have the same base?
Task 7
What is the slope and y-intercept of the line y=x? Select multiple answers.
Task 8
If you shift an exponential function horizontally or vertically, how would this transformation apply to its corresponding logarithmic equation? Talk about it with your partner and make a prediction.
Test your conjecture from Task 8 here by adjusting the sliders c and d
Task 9
Did your conjecture hold true? Explain.
Task 10
Fill in the blanks below:When the bases are the same, a [b][u]horizontal [/u][/b]translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function.[br]When the bases are the same, a [b][u]vertical [/u][/b]translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function.
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Information: Comparing Logarithm and Exponential Functions Graphs