Question

4

Answer 1

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 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 \times f(x)
• Horizontal stretch by a factor k: y = f(\dfrac{x}{k})

Given the function f(x)=2ˣ, while the h(x)=-3(2ˣ), therefore, the function f(x) is a reflection and a translation of a function. Hence, the correct option is D.

Learn more about Transforming functions:

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