Listen
After a horizontal reflection across the $y$-axis, $f(x)$ is:
$f(-x)$
$-4-4$
$-f(x)$
$f(x-1)$
Answer (2)
A horizontal reflection across the y -axis transforms x into − x .
The function f ( x ) becomes f ( − x ) after the reflection.
The correct answer is f ( − x ) .
After a horizontal reflection across the y -axis, f ( x ) is f ( − x ) .
Explanation
Understanding the Problem The problem asks us to identify the transformation of a function f ( x ) after it undergoes a horizontal reflection across the y -axis. We are given four options: f ( − x ) , − 4 − 4 , − f ( x ) , and f ( x − 1 ) .
Applying the Reflection A horizontal reflection across the y -axis means that the x -values are negated. In other words, every x is replaced with − x . Therefore, the function f ( x ) becomes f ( − x ) .
Identifying the Correct Option Comparing this result with the given options, we see that the correct answer is f ( − x ) .
Final Answer Therefore, after a horizontal reflection across the y -axis, f ( x ) becomes f ( − x ) .
Examples
Imagine you are looking at yourself in a mirror. Your reflection is a horizontal reflection across the y-axis. If your right hand is raised, the left hand of your reflection appears to be raised. Similarly, the graph of a function f ( x ) reflected across the y-axis is f ( − x ) . This concept is useful in understanding symmetry and transformations in various fields, such as physics, engineering, and computer graphics.
After a horizontal reflection across the y -axis, the function f ( x ) transforms to f ( − x ) . Therefore, the correct answer is f ( − x ) . This transformation involves negating the x -value in the function's equation.
;
