Linear approximation with interpolation
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Lesson Summary:
In this lesson, you will learn about linear approximation with interpolation. You will understand that any relationship can be modeled linearly if one restricts the domain enough, and how to do linear interpolation to get a quick estimate of the value of the relationship between two points. You will also see how linear interpolation works with a table of input and output values for a relationship, and how to make a new table with interpolated values. This skill will come in handy when you need to estimate an output for an input beyond the data.
Lesson Description:
Understand clearly that ANY relationship can be modeled linearly if one restricts the domain enough.
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Additional Resources:
- Linear Interpolation - An explanation of what linear interpolation is and how it is done.
- Zooming in on cartesian graphs - Zoom into a Cartesian graph of a function and see it looks linear if you look close enough
- Notes - Notes from this lesson.
Questions answered by this video:
- What is linear approximation?
- What is linear interpolation?
- How can you do linear interpolation to approximate the value of a non-linear function by using linear approximation in a small interval of the function?
- How can you zoom in closely to the graph of a function until it looks like a line?
- How can you do linear interpolation between the points (4, 175) and (7, 200) to approximate the value when the input is 5?
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Staff Review
This lesson will show you how any relationship / function can be approximated / modeled with a linear function in certain restrictions of the domain. You will learn to do interpolation to approximate a value at a certain input using a linear relationship in a very small subset of the function.
