Comparing Logarithm and Exponential Functions Graphs
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 where
Now uncheck the Exponential graph and select the Logarithmic graph.
Task 2
Notice the properties of the logarithmic graph. Select all that apply for where
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 horizontal translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function. When the bases are the same, a vertical translation of an exponential function corresponds to a ___________ translation of its corresponding logarithmic function.