Which transformation of f(x)=x^2 is modeled by the function g(x)=-5(4x)^2

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07-12-2022
Mathematics

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Which transformation of f(x)=x^2 is modeled by the function g(x)=-5(4x)^2

Sagot :

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MrRoyal MrRoyal · Answer 1 · 2022-12-09T05:51:46-05:00

The transformations of f(x) are (b) a horizontal shrink by a factor of 1/4, a vertical stretched by a factor of 5 and a reflection across the x-axis

How to describe the transformation from the parent function?

From the question, we have the following function that can be used in our computation:

f(x) = x²

g(x) = -5(4x)²

Mathematically, these equations can be represented as

g(x) = -5f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4
The -5 implies that the function f(x) is vertically stretched by a factor of 5 and then reflected across the x-axis

Hence, the transformed function is (b)

Sagot :

How to describe the transformation from the parent function?

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