Use the Image to answer the question

Question

Given the graph f(x)=(x+3)2
, which of the options is the graph y=−f(x)


(1 point)
Responses

Option 1
Option 1

Option 2
Option 2

Option 4
Option 4

Option 3
Option 3

Answer 1

I can't see images or graphs, but I can help you understand how to determine the graph of \( y = -f(x) \) based on the function you've provided.

The function \( f(x) = (x + 3)^2 \) is a parabola that opens upwards and has its vertex at the point (-3, 0).

When you take the negative of this function, \( y = -f(x) \), you essentially reflect the graph of \( f(x) \) over the x-axis. This means that:

• The vertex of the new graph will be at (-3, 0) (it stays the same horizontally but goes down vertically).
• The parabola will open downwards instead of upwards.

To find the correct option for \( y = -f(x) \):

1. Look for a graph that has the vertex at (-3, 0).
2. Check to see that the parabola opens downwards.

Based on these characteristics, examine the options you have and select the one that matches these criteria. If you describe them to me, I can help you determine the correct answer!