Answered

1. Describe the transformations necessary to transform the graph of
f(x) to that of g(x)
f(x) = x² and g(x) = 3(x - 1)² + 4

Answer :

luisejr77

Answer:  

- The function [tex]f(x)[/tex] must be shifted right 1 unit.

- The function [tex]f(x)[/tex]  must be shifted up 4 units.

- The function [tex]f(x)[/tex]  must be stretched vertically by a factor of 3.

Step-by-step explanation:

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

If [tex]f(x)+k[/tex], then the function is shifted up "k" units.

If [tex]f(x)-k[/tex], then the function is shifted down "k" units.

If [tex]f(x+k)[/tex], then the function is shifted left "k" units.

If [tex]f(x-k)[/tex], then the function is shifted right "k" units.

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

If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], then the function is compressed vertically by a factor of "b".

In this case we have the following parent function [tex]f(x)[/tex] :

[tex]f(x)=x^2[/tex]

And the function [tex]g(x)[/tex]:

[tex]g(x) = 3(x - 1)^2 + 4[/tex]

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

- The function [tex]f(x)[/tex] must be shifted right 1 unit.

- The function [tex]f(x)[/tex]  must be shifted up 4 units.

- The function [tex]f(x)[/tex]  must be stretched vertically by a factor of 3.

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