The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = 125x³
How does transformation of a function happens?
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: [tex]y=f(x+c)[/tex] (same output, but c units earlier)
Right shift by c units: [tex]y=f(x-c)[/tex](same output, but c units late)
Up by d units: [tex]y = f(x) + d[/tex]
Down by d units: [tex]y = f(x) - d[/tex]
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k: [tex]y = f\left (\dfrac{x}{k}\right )[/tex]
For this case, we're specified that:
Original function: y = x³
Transformation: horizontal stretch by a factor of 1/5
Assuming the horizontal axis is having input variable x, and vertical axis having output variable y = x³, and the fact that a function y = f(x) if is horizontally stretched by a factor k, becomes [tex]y = f\left (\dfrac{x}{k}\right )[/tex], we have:
[tex]y = f(x) = x^3 \rightarrow y = f\left( \dfrac{x}{1/5} \right) = f(5x) = (5x)^3 = 125x^3[/tex]
The graph of both the functions is given below.
Thus, the equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = 125x³
Learn more about transforming functions here:
https://brainly.com/question/17006186
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