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Comparing Logarithm and Exponential Functions Graphs

Change the position of the slider in order to change the base a 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 where

Tick all that apply
  • A
  • B
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  • D
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Check my answer (3)

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

Tick all that apply
  • A
  • B
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  • D
  • E
  • F
  • G
  • H
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Check my answer (3)

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.

Tick all that apply
  • A
  • B
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  • E
Check my answer (3)

Task 5

How do the properties of the two function types differ? Select all that apply.

Tick all that apply
  • A
  • B
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  • D
Check my answer (3)

Task 6

What do you notice about the intersection between the exponential and logarithmic graphs when they have the same base?

Tick all that apply
  • A
  • B
  • C
  • D
  • E
Check my answer (3)

Task 7

What is the slope and y-intercept of the line y=x? Select multiple answers.

Tick all that apply
  • A
  • B
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  • F
Check my answer (3)

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.