IB DP Maths: AA HL复习笔记2.9.4 Reciprocal & Square Transformations
What effects do reciprocal transformations have on the graphs?
- The x-coordinates stay the same
- The y-coordinates change
- Their values become their reciprocals
- If y = 0 then a vertical asymptote goes through the original coordinate
- Points that lie on the line y = 1 or the line y = -1 stay the same
How do I sketch the graph of the reciprocal of a function: y = 1/f(x)?
- Sketch the reciprocal transformation by considering the different features of the original graph
- Consider key points on the original graph
Consider key regions on the original graph
Worked Example
Square Transformations
What effects do square transformations have on the graphs?
- The effects are similar to the transformation y = |f(x)|
- The parts below the x-axis are reflected
- The vertical distance between a point and the x-axis is squared
- This has the effect of smoothing the curve at the x-axis
The x-coordinates stay the same- The y-coordinates change
- Their values are squared
- The coordinates (x, y) become (x, y²)
- Points that lie on the x-axis or the line y = 1 stay the same
How do I sketch the graph of the square of a function: y = [f(x)]²?
- Sketch the square transformation by considering the different features of the original graph
- Consider key points on the original graph
Exam Tip
Worked Example
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