Question

If f(x) = x^3 and g(x) = -2x^3, how has f(x) been transformed to get g(x)?

Answer 1

The transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

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 the horizontal axis is the input axis and the 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 = f(x/k)

If f(x) = x³ and g(x) = -2x³, then the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

Hence, the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

Learn more about Transforming functions:

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