Question

If the parent function is f(x) = x2 and its transformed function is g(x) = 2(x − 1)2 + 2, how is the graph of g(x) transformed from the graph of its parent function?

stretch, shift along the y–axis, and shift along the x–axis
shift along the x–axis and the y–axis
reflection only
stretch along the y–axis and reflection through the origin

Answer 1

The answer is A. g(x) is a vertical stretch and shift over both axes.

Answer 2

Option A is the correct choice.

Step-by-step explanation:

We have been given a parent function
`f(x)=x^2` and its transformed function is
`g(x)=2(x-1)^2+2`. We are asked to find the transformation rules used to function f(x) to get g(x).

First of all let us recall the translation rules.

`f(x-a)\rightarrow\text{Graph shifted to the right by a units}`

`f(x)+a\rightarrow\text{Graph shifted upwards by a units}`

`a*f(x)\rightarrow\text{Graph stretches vertically, if a}>1`

Upon looking at transformation rules we can see that the graph of g(x) is vertically stretched by a scale factor of 2. It is also shifted along the y-axis by 2 units upwards and along the x-axis by 1 unit to to the right.

Therefore, option A is the correct choice.