Horizontal shift

Definition

A horizontal shift is a transformation that moves a graph left or right along the x-axis without changing its shape. It is represented by modifying the function as $f(x) \rightarrow f(x - h)$, where $h$ is the number of units shifted.

5 Must Know Facts For Your Next Test

1. If $h > 0$, the graph shifts to the right by $h$ units.
2. If $h < 0$, the graph shifts to the left by $|h|$ units.
3. Horizontal shifts do not affect the vertical position of key points on the graph.
4. The equation for horizontal shift in exponential functions is $a \cdot b^{(x-h)}$.
5. In trigonometric functions, such as sine and cosine, horizontal shifts change the phase of the wave.

Review Questions

• How does a positive value of $h$ affect a function’s graph in a horizontal shift?
• What transformation occurs if you replace $x$ with $(x + 3)$ in a function?
• Explain how horizontal shifts impact periodic functions like sine and cosine.

Related terms

Vertical Shift: A transformation that moves a graph up or down along the y-axis without changing its shape.

Phase Shift: A type of horizontal shift specific to periodic functions, altering their starting point on the x-axis.

Transformation: An operation that moves or changes a function's graph while maintaining its overall shape.