Horizontal reflection

Definition

A horizontal reflection is a transformation that flips a function's graph over the y-axis. Mathematically, it changes the function $f(x)$ to $f(-x)$.

5 Must Know Facts For Your Next Test

1. The horizontal reflection of a point $(x, y)$ on the graph of $f(x)$ will be $(-x, y)$.
2. Horizontal reflections do not change the y-coordinates of points on the graph.
3. The equation for a horizontally reflected function is $y = f(-x)$.
4. Horizontal reflections affect even and odd functions differently; even functions remain unchanged while odd functions are inverted.
5. To graph a horizontal reflection, simply reflect all points across the y-axis.

Review Questions

• What is the result of applying a horizontal reflection to the function $f(x) = x^2$?
• How does a horizontal reflection affect an odd function such as $f(x) = x^3$?
• If you have a point $(3, -2)$ on the graph of $f(x)$, where will this point be after applying a horizontal reflection?

Related terms

Vertical Reflection: A transformation that flips a function’s graph over the x-axis, changing $f(x)$ to $-f(x)$.

Vertical Stretch: A transformation that scales the graph of a function vertically by multiplying by a factor greater than one.

Horizontal Translation: $Shift$ing every point of a function's graph left or right by adding or subtracting from its input variable.