The transformation of a function may involve any change. The correct option is D.
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 given function f(x)=x² is transformed to h(x)=(1/8)x^2-13, therefore, the graph or f(x) is horizontally stretched by a factor of 8 and shifted 13 units to the right.
Hence, the correct option is D.
Learn more about Transforming functions:
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