Horizontal reflection

Definition

A horizontal reflection is a transformation that flips a function's graph over the y-axis. It changes the sign of the x-coordinates of all points on the graph.

5 Must Know Facts For Your Next Test

1. The horizontal reflection of a function $f(x)$ is given by $f(-x)$.
2. Horizontal reflections do not affect the y-values, only the x-values are negated.
3. If $f(x)$ is an even function, its graph remains unchanged after a horizontal reflection.
4. For odd functions, a horizontal reflection results in the same graph as a vertical reflection.
5. To identify a horizontal reflection in an equation, look for a negative sign inside the argument of the function, e.g., $f(-x)$.

Review Questions

• What is the result of applying a horizontal reflection to the function $f(x) = x^2$?
• How does performing a horizontal reflection affect an even function compared to an odd function?
• Given $g(x) = \sin(x)$, what would be the equation after applying a horizontal reflection?

Related terms

Vertical Reflection: A transformation that flips a function's graph over the x-axis, changing the sign of all y-coordinates.

Even Function: A function where $f(-x) = f(x)$ for all x in its domain; symmetric about the y-axis.

Odd Function: $A function where f(-x) = -f(x) for all x in its domain; symmetric about the origin.$