Question

reflections about the y - axis quick check
if the function $f(x)=(x + 1)^2$ is reflected horizontally, how does the reflection affect the point $(-2,1)$? (1 point)
in the horizontal reflection, the point $(-2,1)$ becomes $(2,-1)$.
in the horizontal reflection, the point $(-2,1)$ becomes $(-2,-1)$.
in the horizontal reflection, the point $(-2,1)$ becomes $(2,1)$.
in the horizontal reflection, the point $(-2,1)$ becomes $(1,2)$.

Explanation:

Step1: Recall reflection rule

A horizontal reflection (reflection about the y - axis) changes the sign of the x - coordinate of a point while keeping the y - coordinate the same. The rule for reflecting a point $(x,y)$ about the y - axis is $(x,y)\to(-x,y)$.

Step2: Apply rule to given point

For the point $(-2,1)$, when we apply the reflection about the y - axis rule, $x=-2$ and $y = 1$. The new x - coordinate is $-(-2)=2$ and the y - coordinate remains $1$. So the new point is $(2,1)$.

Answer:

In the horizontal reflection, the point $(-2,1)$ becomes $(2,1)$.