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state the various transformations applied to the base function F(x) = x2 to obtain a graph of the function g(x) = -2[(x - 1)2 + 3).

User Sfotiadis
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1 Answer

2 votes

Answer:

A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift right by 1 unit, and a vertical translation downward by 6 units.

Step-by-step explanation:

The parent function is given as:


f(x)=x^2

We can write the transformation g(x) in the form below:


\begin{gathered} g\mleft(x\mright)=-2\mleft[\mleft(x-1\mright)^2+3\mright] \\ =-2(x-1)^2-6 \end{gathered}

A horizontal shift right by 1 unit gives:


(x-1)^2

A vertical translation down by 6 units gives:


(x-1)^2-6

A reflection about the x-axis gives:


-(x-1)^2-6

Finally, a vertical stretch by a factor of 2 gives:


g(x)=-2(x-1)^2-6

So, the transformation is:

A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift right by 1 unit, and a vertical translation downward by 6 units.

Option 3 is correct.

User Unki
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