Question

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).

Answer 1

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.