The transformation of a function may involve any change. The function with the graph are given below.
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units: y=f(x+c) (same output, but c units earlier)
- Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
The real graph of the function is f(x)=x², now if the graph of the given function can be found by using the transformation rule as shown above. The function with the graph are given below.
Learn more about Transforming functions:
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