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Inverse Graphs
Age 18 · Maths
The natural logarithm undoes the exponential function. Their graphs are reflections of each other across the line y = x.
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In the picture
- Steep rising curve: rises from lower left and continues upward to the right
- Slow rising curve: hugs the vertical axis below the origin and rises slowly to the right
- Dashed diagonal line: passes through the origin at forty-five degrees
- Point on the vertical axis: one unit above the origin
- Point on the horizontal axis: one unit right of the origin
Examples
- Compound interest grows exponentially, and a natural logarithm can estimate how long it takes for an investment to reach a target.
- A cooling drink loses its temperature difference exponentially, and a natural logarithm can estimate the elapsed cooling time.
Key takeaways
- The natural logarithm and the exponential function undo each other.
- Their graphs are mirror images across the line y = x.
Quiz: Inverse Graphs (Age 18)
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What is the relationship between the natural logarithm and the exponential function?
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Across which line are the graphs of the natural logarithm and the exponential function mirror images?
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What does the natural logarithm undo?
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