Reflect the function f(x)=(x+1)2

Question

about the origin. What is the position of the point (−4,9)
in the reflected function?(1 point)
The point (−4,9)
reflects to (
,
) in −f(−x)
.

Answer 1

To reflect the function $f(x)=(x+1{)}^2$ about the origin, we need to transform both $x$ and $y$ coordinates. This is done by replacing $f(x)$ with $-f(-x)$.

First, let's calculate $f(-x)$: $$f(-x)=(-x+1{)}^2=(1-x{)}^2$$

Now we can find $-f(-x)$: $$-f(-x)=-(1-x{)}^2$$

Next, we reflect the point $(-4,9)$. The x-coordinate after reflection will be $x^{\prime }=-(-4)=4$. The original y-coordinate $y=9$ will become $y^{\prime }=-9$.

Now, we compute the new point: So, the reflected point is $(4,-9)$.

In conclusion, the point $(-4,9)$ reflects to $(4,-9)$ in the function $-f(-x)$.