Final answer:
Vertical and horizontal shifts in mathematics refer to moving the graph of a function upwards or downwards, and left or right in the coordinate system respectively. To apply these shifts, constants are added or subtracted from the function's formula.
Step-by-step explanation:
Understanding vertical and horizontal shifts is essential when working with functions and graphs in mathematics. A vertical shift refers to moving the graph of a function up or down in the coordinate system, while a horizontal shift refers to moving the graph left or right.
- Vertical shift up means the function's graph is moved upwards in the coordinate system.
- Vertical shift down means the graph is moved downwards in the coordinate system.
- Horizontal shift left means the graph is moved to the left side of the coordinate system.
- Horizontal shift right means the graph is moved to the right side of the coordinate system.
To apply these shifts algebraically, you would add or subtract constants from the function's formula. For example, to shift the graph of f(x) up by k units, you would calculate f(x) + k. For a shift to the left by h units, you would use f(x + h).