205k views
4 votes
If (2,6) is a point on the graph of y=f(x) and g(x)=-f(x+3). which point must lie on the graph of y=g(x)?

(A) (-1,6)

(B) (-1,-6)

(C) (5,-6)

(D) (-5,6)

User Nitzien
by
8.1k points

1 Answer

2 votes

Final answer:

To find the corresponding point on the graph of y=g(x), we must apply the transformation g(x)=-f(x+3) to the point (2,6). This results in a new point of (-1, -6) after reflecting over the x-axis and shifting left by three units, which matches choice (B).

Step-by-step explanation:

The student is asking about transformation of functions, specifically how a transformation affects points on the graph of the original function. Since the original function f(x) has a point (2,6), we want to find where this point will be mapped on the function g(x), which is defined as g(x) = -f(x+3). This involves a horizontal shift to the left by 3 units (since we're adding 3 inside the function) and a reflection across the x-axis (because of the negative sign in front of the function).

The point (2,6) on f(x) means that f(2)=6. Using the definition of g(x), we find that g(x) = -f(x+3) = -f(2) when x=-1 because -1 + 3 = 2. Since f(2)=6, g(-1) = -6, so the point on the g(x) function will be (-1, -6), which corresponds to answer choice (B).

User Theister
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories