Question

Graph the function f of x equals x + 1 and the function of its horizontal reflection what is the position of the point negative 4, 9 and the reflected function the point negative 4, 9 reflects to blank and f of negative X

Answer 1

To reflect the function \( f(x) = x + 1 \) horizontally, we need to understand that reflecting a function horizontally means replacing \( x \) with \( -x \). This gives us the new function:

\[
f(-x) = -x + 1.
\]

Now, we need to check the original function \( f(x) \) and the reflected function \( f(-x) \):

1. **Original Function:**
\[
f(x) = x + 1
\]

For example, the point \((-4, 9)\) corresponds to \( f(-4) = -4 + 1 = -3\). However, since this is not directly part of our reflection process, let's focus on just finding the reflection.

2. **Reflected Function:**
\[
f(-x) = -x + 1.
\]

Now, to find the reflected position of the point \((-4, 9)\):

- The \( x \)-coordinate will also reflect over the vertical axis (the y-axis), which means we will change \(-4\) to \(4\).

Next, we need to find the \( y \)-coordinate of the point \((4, y)\) in the reflected function \( f(-x) \):

- Substitute \( x = 4 \) into \( f(-x) \):
\[
f(-4) = -(-4) + 1 = 4 + 1 = 5.
\]

Thus, the reflection of the point \((-4, 9)\) in \( f(-x) \) is:

\[
(4, 5).
\]

So to summarize:

- The original point \((-4, 9)\) reflects to the point \((4, 5)\) in the function \( f(-x) \).