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suppose that G(x)=F(x+2) which statement best compares the graph of G(x) with the graph of F(x) A. the graph of G(x) is the graph of F(x) shifted 2 units to the right B thr graph of G(x) is the graph​ of F(x) shifted 2 units down C the graph of G(x) is the graph of F(x) shifted 2 units up D the graph of G (x) is the graph of f(x) shifted 2 units to the left

suppose that GxFx2 which statement best compares the graph of Gx with the graph of Fx A the graph of Gx is the graph of Fx shifted 2 units to the right B thr gr class=

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Answer:

Last option is the correct answer:

The  graph of G (x) is the graph of f(x) shifted 2 units to the left

Step-by-step explanation:

We know that for any parent function f(x) the graph of the transformed function:

[tex]g(x)=f(x+a)[/tex]

is a shift of the the parent function f(x) either to the left or the right depending on the value of a.

if a>0 then the shift is 'a' units to the left

and if a<0 then the shift is 'a' units to the right.

Here we have transformed function G(x) as:

[tex]G(x)=F(x+2)[/tex]

i.e. a=2>0.

Hence, the  graph of G (x) is the graph of f(x) shifted 2 units to the left.

Using translation concepts, it is found that the correct option regarding the comparison of he graph of G(x) with the graph of F(x) is given by:

D the graph of G (x) is the graph of f(x) shifted 2 units to the left.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the possible translations that can be made to the function are:

  • 2 units up: G(x) = F(x) + 2.
  • 2 units down: G(x) = F(x) - 2.
  • 2 units to the left: G(x) = F(x + 2).
  • 2 units to the right: G(x) = F(x - 2).

Hence option D, which is a shift of 2 units to the left, is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517

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