the function G(x)=f(x+3)+2 which of the following is true of the graph of g(x)?

A the graph of g(x) is shifted 3 units to the right and 2 units above the graph of F(x)

B The Graph of g(x) is shifted 3 units to the left and 2 units above the graph f(x)

C the graph of g(x) is shifted 3 units to the right and 2 units below the graph of f(x)

D The graph of g(x) is shifted 3 units to the left and 2 units below the graph of F(x)

g(x)=(x+3)+2

G(x) = (x-h) + k
h translates the graph left/right and k translates the graph up/down.
Because the equation is x- the parenthesis is (x - - 3) which makes h a negative 3 and will translate left. The k positive so it will move up.
Letter B

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-04-26T13:25:49-04:00

In option (B) the Graph of g(x) is shifted 3 units to the left, and 2 units above the graph f(x) is correct.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

g(x) = f(x+3) +2

If we have f(x) as a parent function.

If we replace x with x+3 the graph of g(x) will shift to the 3 units left.

g(x) = f(x+3)

If we add 2 to the function it will shift 2 units above the graph of f(x)

g(x) f(x+3) + 2

The transformation can be shown in the picture(supposing the f(x) = x²)

Thus, in option (B) the Graph of g(x) is shifted 3 units to the left, and 2 units above the graph f(x) is correct.

Learn more about the function here:

brainly.com/question/5245372