Question

If g(x)=x^2 but it has been stretched and shifted, which of the following could be the equation of f(x)?

Answer 1

Case: Function transformation

Given:

A graph of x^2 transformed

Method:

Steps of transformation

`y=(ax)^2+b`

1. Stating the parent function

`y=x^2`

2. Translating a step-down mean s b= -1

`y=x^2-1`

3. Since the function is stretched, the a picks up a value less than 1

`y=((3)/(4)x)^2-1`

Above is the only suitable fraction option from above, as a=3/4 and b=-1.

Final answer: Option (D)

`f(x)=((3)/(4)x)^2-1`