Question

1. Describe the transformations necessary to transform the graph of

Answer 1

Answer:  

- The function $f(x)$ must be shifted right 1 unit.

- The function $f(x)$  must be shifted up 4 units.

- The function $f(x)$  must be stretched vertically by a factor of 3.

Step-by-step explanation:

There are some transformations for a function f(x):

If $f(x)+k$, then the function is shifted up "k" units.

If $f(x)-k$, then the function is shifted down "k" units.

If $f(x+k)$, then the function is shifted left "k" units.

If $f(x-k)$, then the function is shifted right "k" units.

If $bf(x)$ and $b>1$, then the function is stretched vertically by a factor of "b".

If $bf(x)$ and $0$, then the function is compressed vertically by a factor of "b".

In this case we have the following parent function $f(x)$ :

$f(x)=x^2$

And the function $g(x)$:

$g(x) = 3(x - 1)^2 + 4$

Based on the explained before, we can describe  the transformations necessary to transform the graph of $f(x)$  to the graph of $g(x)$ :

- The function $f(x)$ must be shifted right 1 unit.

- The function $f(x)$  must be shifted up 4 units.

- The function $f(x)$  must be stretched vertically by a factor of 3.