Question

If the function f of x equals (x + 1)^2 is reflected horizontally how does the reflection affect the point negative 2, 1

Answer 1

To understand how a horizontal reflection affects the function \( f(x) = (x + 1)^2 \) and the point \((-2, 1)\), we need to clarify what a horizontal reflection means.

A horizontal reflection of a function \( f(x) \) is done by replacing \( x \) with \(-x\). As a result, the new function becomes:

\[
g(x) = f(-x) = ((-x) + 1)^2 = (1 - x)^2
\]

Now, let's analyze how this transformation affects the point \((-2, 1)\):

1. **Original Point**: The point \((-2, 1)\) is on the original function \( f(x) \). To check this, substitute \( x = -2 \):

\[
f(-2) = (-2 + 1)^2 = (-1)^2 = 1
\]

So, indeed, the point \((-2, 1)\) is on the graph of \( f(x) \).

2. **Finding the New Point for \( g(x) \)**: Now, we reflect horizontally which means we find the corresponding point in the new function \( g(x) \).

To find the \( x \)-coordinate in the new function, we take the opposite of the original \( x \):

\[
x' = -(-2) = 2
\]

3. **Finding the New \( y \)-Coordinate**: Now substitute \( x' = 2 \) into \( g(x) \):

\[
g(2) = (1 - 2)^2 = (-1)^2 = 1
\]

Thus, the new point after the horizontal reflection is \((2, 1)\).

### Conclusion:
After reflecting the function \( f(x) = (x + 1)^2 \) horizontally, the point \((-2, 1)\) changes to \((2, 1)\).