On a coordinate plane, a cubic root function is shown. It has a point of inflection at (0, -4). Then the equation will be y = - x³ - 4.
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), stretching (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 × f(x)
Horizontal stretch by a factor k: y = 1/k × f(x)
The graph is given below.
y = x³
On a coordinate plane, a cubic root function is shown. It has a point of inflection at (0, -4). Then the equation will be
y = - x³ - 4
Learn more about transforming functions here:
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