Question

I need help with this question please. Ignore the words below it, they’re just part of option A. I also have options to choose from.

Answer 1

We have a guide graph:

`f(x)=x^2`

but this function undergoes a series of transformations after altering the function to be expressed as follows

`g(x)=3(x-1)^2+2`

For this, we must remember the function transformation rules.

1.

`y=g(x-c)`

Where "c" units are moved horizontally to the right.

That is to say that in our function g(x) the function describes a translation of one unit to the right.

2.

`y=g(x)+c`

Where "c" units are moved vertically upwards.

That is to say that in our function g(x) the function describes a translation of two units to upwards

3.

`y=c\cdot g(x)`

Where if c>1 it vertically stretches the graph of y=g(x) by a factor of "c".

That is to say that our function has a vertical stretch by a factor of 3.

In conclusion, the option that meets a vertical stretch with a factor of 3 and a translation of 1 unit to the right and 2 units upward is option C.