Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x + 3)2 + 4?

left 3, up 4
right 3, down 4
left 3, down 4
right 3, up 4

we know that

the vertex in the function f(x) is the point

the vertex in the function g(x) is the point

so

the rule of the transformation that occurs from  f(x) to g(x) is

that means

units left and units up

therefore

the answer is the option

left 3, up 4

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: